K. O. Bowman's Publications

Technical Reports

[1] Bowman, K. O. and David, H. A. (1962), Estimation of the Strength of a Radioactive Source, Virginia Polytechnic Institute, Technical Report No. 54.

[2] Bowman, K. O. and Shenton, L. R. (1965), Asymptotic Covariances for the Maximum Likelihood Estimators of the Parameters of a Negative Binomial Distribution, K-1643.

[3] Bowman, K. O. and Shenton, L. R. (1965), Biases and Covariances of Maximum Likelihood Estimators, K-1633.

[4] Bowman, K. O. and Shenton, L. R. (1966), Biases of Estimator for the Negative Binomial Distribution, ORNL-4005.

[5] Kastenbaum, M. A. and Bowman, K. O. (1966), The Minimum Significant Number of Successes in a Binomial Sample, ORNL- 3909.

[6] Uppuluri, V. R. R. and Bowman, K. O. (1966), Likelihood Ratio Test Criterion for Small Samples from Multinomial Distribution, ORNL-3991.

[7] Uppuluri, V. R. R. and Bowman, K. O. (1966), Data on Set of Trinomial Distribution, ORNL-4004.

[8] Bowman, K. O. and Shenton, L. R. (1967), Remarks on Estimation Problems for the Parameters of the Neyman Type A Distribution, ORNL-4102.

[9] Shenton, L. R. and Bowman, K. O. (1967), "Sampling Moments of Moment and Maximum Likelihood Estimators for Discrete Distribution," Computer Center, University of Georgia, Technical Reprint Series 1.

[10] Bowman, K. O. and Shenton, L. R. (1968), Properties of Estimators for the Gamma Distribution, CTC-1.

[11] Gosslee, D. G. and Bowman, K. O. (1968), Evaluation of Maximum Likelihood Estimates of Parameters in Mixture of Normal Distribution, ORNL-TM-2110.

[12] Bowman, K. O. and Shenton, L. R. (1969), Factorable Determinants, CTC-10.

[13] Bowman, K. O. and Shenton, L. R. (1969), Moments of Moments and Frequencies, CTC-13.

[14] Kastenbaum, M. A., Hoel, D. G. and Bowman, K. O. (1969), Sample Size Requirements: Tests of Equality of Several Gaussian Means, ORNL-4468.

[15] Shenton, L. R., Bowman, K. O. and Hutcheson, K. (1969), Comments on the Distribution of Indices of Diversity, CTC-14.

[16] Bowman, K. O. and Shenton, L. R. (1970), Small Sample Properties of Estimator for the Gamma Distribution, CTC-28.

[17] Kastenbaum, M. A., Hoel, D. G. and Bowman, K. O. (1970), Adequate Sample Size for Randomized Block Designs, ORNL-4527.

[18] Bowman, K. O. (1971), Sample Size Requirement: Continuation, ORNL-4712.

[19] Bowman, K. O. and Shenton, L. R. (1971), Note on Fisher's Linkage Estimation Problem, ORNL-4701.

[20] Bowman, K. O. and Shenton, L. R. (1971), Tables of Moments of the Maximum Likelihood Estimators of the Parameter p for Zero Truncated Binomial Distribution, ORNL-4747.

[21] Dusenberry, W. E. and Bowman, K. O. (1973), Percentage Points of Moment Estimators which are Ratio with an Application to the Shape Parameter of the Gamma Distribution, ORNL-4876.

[22] Handley, B. J. and Bowman, K. O. (1973), An Examination of Several Methods of Estimation for ABO Blood Groups, CTC-58.

[23] Bowman, K. O., Beauchamp, J. J. and Miller, F. L. (1975), Statistical Analysis of Environmental Data, CSD-INF-64.

[24] Bowman, K. O. and Shenton, L. R. (1975), Tables of Moments of the Skewness and Kurtosis Statistics in Nonnormal Sampling, CSD-8.

[25] Shenton, L. R. and Bowman, K. O. (1976), Summable Asymptotic Series, ORNL/CSD 6.

[26] Bowman, K. O. (1980), One Aspect of the Statistical Evaluation of a Computer Model, ORNL/CSD-52.

[27] Bowman, K. O. and Shenton, L. R. (1981), Estimation Problems Associated with the Weibull Distribution, ORNL/CSD-79.

[28] Bowman, K. O. and Shenton, L. R. (1981), "Moment (sqrt(b1), b2) Techniques," ORNL/CSD-83.

[29] Bowman, K. O. and Leach, E. L. (1983), "Confidence limits for the expectation of a Poisson variable," ORNL/CSD-115.

[30] Bowman, K. O. and Shenton L. R. (1983), "The Distribution of the Standard Deviation and Skewness in Gamma Sampling - A New Look at a Craig-Pearson Study," ORNL/CSD-109.

[31] Bowman, K. 0., Shenton, L. R. and Kastenbaum, M. A. (1991), "Discrete Pearson Distribution," ORNL/TM-11899.

[32] Nanstad, R. K., Haggag, F. M., McCabe, D. E., Iskandeer, S. K., Bowman, K. O. and Menke, B. H. (1992), "Irradiation Effects on Fracture Toughness of Two High-Copper Submerged-Arc Welds, HSSI Series 5", ORNL/TM-12156/V1.

[33] Bowman, K. O., Shenton, L. R., Kastenbaum, M. A. and Broman, Karl (1992). "Overdispersion: Notes on Discrete Distributions", ORNL/TM-12167.

[34] Nanstad, R. K., Haggag, F. M., McCabe, D. E. Downing, D. J. and Bowman, K. O. (1993). "Kic Curve in High-Copper Welds", NUREG/CR-5591, ORNL/TM-11568/V1&N2, Vol.1, No.2.

[35] Bowman, K. O., Kastenbaum, M. A., and Shenton, L. R. (1996), Fitting Multi-Parameter Distributions to Human Chromosome Data, Technical Report Number 96-3, Department of Statistics, University of Georgia.

[36] Bowman, K. O. and Shenton, L. R. (1996), The Beta Distribution and Its Four Parameters: A Karl Pearson Centenary Paper, Technical Report Number 96-14, Department of Statistics, University of Georgia.

[37] Bowman, K. O., Shenton, L. R. and Gailey, P. C. (1996), Distribution of the Ratio of Gamma Variate, Technical Report Number 96-18, Department of Statistics, University of Georgia.

[38] Bowman, K. O. and Williams, P. T. (2000). Technical Basis for Statistical Models of Extended K(Ic) and K(Ia) Fracture Toughness Databases for RPV Steels, ORNL/NRC/LTR-99/27.

[39] Bowman, K. O. and Shenton, L. R. (2000), Weibull Distributions When the Shape Parameter is Defined, Technical Report Number 2000-21, Department of Statistics University of Georgia.

[40] Bowman, K. O. and Shenton, L. R. (2001), Mixture of Distributions with Invariant Shape Components, Technical Report, Department of Statistics, University of Georgia.

[41] Bowman, K. O. and Shenton, L. R. (2003), Sample size assessment and the two component Poisson mixture, proportion known, Technical Report Number 2003-7, Department of Statistics, University of Georgia.

[42] Bowman, K. O. and Shenton, L. R. (2003), Canonical dichotomized alternant determinants and Poisson mixtures, Technical Report Number 2003-8, Department of Statistics, University of Georgia.

[43] Bowman, K. O. and Shenton, L. R. (2004), The Asymptotic variance and Skewness of Maximum Likelihood Estimators Using Maple, Technical Report Number 2004-1, Department of statostocs. University of Georgia.

[44] Bowman, K. O. and Shenton, L. R. (2007), The Difference Calculas and the Negative Binomial Distribution, Technical Report Number 2007-1, Department of statostocs. University of Georgia.

Journal Articles:

[1] Shenton, L. R. and Bowman, K. O. (1963), "Higher Moments of a Maximum-Likelihood Estimator", J. Roy. Statist. Soc., Ser. B., 25, 305-317.

[2] Shenton, L. R. and Bowman, K. O. (1967), "Remarks on Large Sample Estimators for Some Discrete Distributions," Technometrics, 9, 587-598.

[3] Newell, Guy R., Harris, W. W., Bowman, K. O., Boone, C. W. and Anderson, N. G. (1968), "Evaluation of 'Virus-Like' particles in the Plasmas of 255 Patients with Leukemia and Related Diseases," New Eng. J. of Med., 278, 1185-1191.

[4] Shenton, L. R. and Bowman, K. O. (1969), "Maximum Likelihood Estimator Moments for the Two-Parameter Gamma Distribution," Sankhya Ser. B, 31, Pts. 3 and 4, 379-396.

[5] Bowman, K. O. and Shenton, L. R. (1970), "Properties of the Maximum Likelihood Estimator for the Parameter of the Logarithmic Series Distribution," Random Counts in Scientific Work, 1, ed., G. P. Patil, Pennsylvania State University Press, 127-150.

[6] Kastenbaum, M. A. and Bowman, K. O. (1970), "Tables for Determining the Statistical Significance of Mutation Frequencies," Mut. Res., 9, 527-549.

[7] Kastenbaum, M. A., Hoel, D. G. and Bowman, K. O. (1970), "Sample Size Requirement: One Way Analysis of Variance," Biometrika, 57, 421-430.

[8] Kastenbaum, M. A., Hoel, D. G. and Bowman, K. O. (1970), "Sample Size Requirement: Randomized Block Design," Biometrika, 57(3), 573-577.

[9] Shenton, L. R. and Bowman, K. O. (1970), "Remarks on Thom's Estimators for the Gamma Distribution," Monthly Weather Rev., 98(2), 154-160.

[10] Shenton, L. R. and Bowman, K. O. (1970), "Tables of the Moments of the Maximum Likelihood Estimators of the Two Parameter Gamma Distribution," Rep. Statist. Appl. Res., JUSE, 17(3), 25-44.

[11] Bowman, K. O. and Shenton, L. R. (1971), "Small Sample Properties of the Maximum Likelihood Estimator Associated with Fisher's Linkage Problem," Jour. Stat. Comput. and Simulation, 1, 71-85.

[12] Shenton, L. R. and Bowman, K. O. (1971), "Continued Fractions for the PSI Function and Its Derivatives," SIAM Jour. Appl. Math., 20(4), 547-554.

[13] Shenton, L. R. and Bowman, K. O., and Sheehan, D. (1971), "Sampling Moments of Moments Associated with Univariate Distribution," JRSS Ser. B, 33, 444-457.

[14] Bowman K. O. (1972), "Tables of the Sample Size Requirement," Biometrika, 59, 234.

[15] Bowman, K. O. and Shenton, L. R. (1972), "Factorable Determinant," The Math Mag., 45(3), 144-147.

[16] Shenton, L. R. and Bowman, K. O. (1972), "Further Remarks on Maximum Likelihood Estimators for the Gamma Distribution," Technometrics, 14, 725-733.

[17] Bowman, K. O. (1973), "Power of the Kurtosis Statistic (b2) in Tests of Departures from Normality," Biometrika, 60, 623-628.

[18] Bowman, K. O. and Shenton, L. R. (1973), "Notes on the Distribution of sqrt(b1) in Sampling from Pearson Distributions," Biometrika, 60, 155-167.

[19] Bowman, K. O. and Shenton, L. R. (1973), "Remarks on the Distribution of Karl Pearson's k-Statistic, k = 2b2 - 3b1 - 6," Bull. Internat. Statist. Inst. Proc. of the 39th Session, Vol. XLV, Book 1, 210-218.

[20] Bowman, K. O. and Shenton. L. R. (1973), "Space of Solutions for a Normal Mixture," Biometrika, 60, 629-636.

[21] Shenton, L. R. and Bowman, K. O. (1973), "Notes on the Sample Size to Achieve Normality for Maximum Likelihood Estimators for the Gamma Distribution," Monthly Weather Rev., 101(12), 891-892.

[22] Bowman, K. O. and Shenton, L. R. (1973), "Remarks on the Distribution of sqrt(b1) in Sampling from a Normal Mixture and Normal Type A Distribution," J. Amer. Statist. Assoc., 68, 998-1003.

[23] Bowman, K. O. and Kastenbaum, M. A. (1974), "Potential Pitfalls of Portable Power," Technometrics, 16(3), 349-353.

[24] Patel, Y. C., Shenton, L. R. and Bowman, K. O. (1974), "Maximum Likelihood Estimation for the Parameters of the Hermite Distribution," Sankhya, 36, 154-162.

[25] Bowman, K. O. and Beauchamp, J. J. (1975), "Pitfalls with Some Gamma Variate Simulation Routines," J. Statist. Comput. Simulation, 4, 141-154.

[26] Shenton, L. R. and Bowman, K. O. (1975), "Johnson's SU and the Skewness and Kurtosis Statistic," J. Amer. Statist. Assoc., 70, 220- 228.

[27] Bowman, K. O. and Shenton, L. R. (1975), "Omnibus" Test Contours for Departures from Normality Based on sqrt(b1) and b2, Biometrika, 62, 243-250.

[28] Shenton, L. R. and Bowman, K. O. (1975), "The Development of Techniques for the Evaluation of Sampling Moments," Internat. Statist. Rev., 43(3), 317-334.

[29] Shenton, L. R. and Bowman, K. O. (1976), "A New Algorithm for Summing Divergent Series Part I. Basic Theory and Illustrations," Journal of Computational and Applied Mathematics, 2, 151-167.

[30] Bowman, K. O. and Shenton, L. R. (1976), "A New Algorithm for Summing Divergent Series Part II. A Two-Component Borel Summability Model," Journal of Computational and Applied Mathematics, 2, 259-266.

[31] Bowman, K. O., Beauchamp, J. J. and Shenton, L. R. (1977), "The Distribution of the t-Statistic Under Non-Normality ," International Statistical Review, 45, 233-242.

[31] Dusenberry, W. E. and Bowman, K. O. (1977), "The Moment Estimator for the Shape Parameter of the Gamma Distribution," Comm. Stat. Part B., Simulation and Computation, 6, 1-19.

[32] Pearson, E. S., D'Agostino, R. B. and Bowman, K. O. (1977), "Test for Departure from Normality: Comparison of Powers," Biometrika, 64, 231-246.

[33] Shenton, L. R. and Bowman, K. O. (1977), "A Bivariate Model for the Distribution of sqrt(b1) and b2," Journal of the American Statistical Association, 72, 206-211.

[34] Shenton, L. R. and Bowman, K. O. (1977), "A New Algorithm for Summing Divergent Series Part III: Application," Journal of Computation and Applied Mathematics, 3, 35-51.

[35] Bowman, K. O. and Shenton, L. R. (1978), "Asymptotic Series and Stiltjies Continued Fractions for a Gamma Function Ratio, Journal of Computation and Applied Mathematics, 4, 105-111.

[36] Shenton, L. R. and Bowman, K. O. (1978), "Generalized Continued Fractions and Whittaker's Approach," Journal of Computation and Applied Mathematics, 4, 3-5.

[37] Bowman, K. O. and Shenton, L. R. (1979), "Approximate Percentage Points for Pearson Distribution," Biometrika, 66, 147-151.

[38] Bowman, K. O. and Shenton, L. R. (1979), "Further Approximate Pearson Percentage Points and Cornish-Fisher," Comm. Stat. Part B, Simulation and Computation, B(8), 231-244.

[39] Shenton, L. R., Bowman, K. O. and Lam, H. K. (1979), "Comments on a paper by Geary," Biometrika, 66, 400-401.

[40] Bowman, K. O. and Shenton, L. R. (1980), "Evaluation of the Parameter of SU by Rational Fractions," Comm. Stat. Part B, Simulation and Computation, B(9), 127-132.

[41] Bowman, K. O., Shenton, L. R. and Lam, H. K (1980), "Moments of the Ratio Mean Deviation/Standard Deviation under Normality--A New Look," Rep. Stat. Appl. Res., Union of Japanese Scientists and Engineers, 27, 1-15.

[42] Patrinos, A. A. N. and Bowman, K. O. (1980), "Weather Modification from Cooling Tower: A Test Based on the Distributional Properties of Rainfall," Journal of Applied Meterology, 19(3), 290-297.

[43] Bowman, K. O., Serbin, C. A. and Shenton, L. R. (1981), "Explicit Approximate Solutions for SB," Comm. Stat. Part B, Simulation and Computation, B(10), 1-15.

[44] Bowman, K. O. and Shenton, L. R. (1981), "Explicit Accurate Approximations for the Parameter of LU," Statistical Distribution in Scientific Work, Vol. 5, ed., C. Taillie et al., 231-240.

[45] Bowman, K. O. and Shenton, L. R. (1982), "Approximations to Distributions," Encyclopedia of Statistical Sciences, Vol. 1, ed., Samuel Kotz and N. L. Johnson, John Wiley and Sons, Inc., 107-118.

[46] Bowman, K. O. and Shenton, L. R. (1982), "Properties of Estimators for the Gamma Distribution," Communications in Statistics B - Simulation and Computation, B11, 377-519.

[47] O'Neill, J. P. and Bowman, K. O. (1982), "Effect of Selection Cell Density on the Recovery of Mutagen-Induced 6-Thioguanine-Resistant Cells," Environ. Mutagenesis, Vol. 4, 627-637.

[48] Shenton, L. R. and Bowman, K. O. (1982), "A Lagrange Expansion for the Parameters of Johnson's SU," Journal of Statistical Computation and Simulation, 15, 89-95.

[49] Bowman, K. O. and Shenton, L. R. (1983), "Johnson's Translation System," Encyclopedia of Statistical Sciences, Vol. 4, ed., Samuel Kotz and N. L. Johnson, John Wiley and Sons, Inc., 303-314.

[50] Bowman, K. O. and Shenton, L. R. (1983), "Levin's Summation Algorithm," Encyclopedia of Statistical Sciences, Vol. 4, ed., Samuel Kotz and N. L. Johnson, John Wiley and Sons, Inc., 611-617.

[51] Bowman, K. O. and Shenton, L. R. (1983),"Continued Fractions and the Polygamma Functions," Journal of Computational and Applied Mathematics, Vol. 9, 29-39.

[52] Bowman, K. O. and Shenton, L. R. (1983), "Maximum Likelihood Estimators for the Gamma Distribution Revisited," Communications in Statistics, B, 12(6), 697-710.

[53] Bowman, K. O. (1984), "Extended Moment Series and the Parameters of the Negative Binomial Distribution," Biometrics, Vol. 40, 249-252.

[54] Bowman, K. O. (1984), "Computation of the Polygamma Functions," Communications in Statistics, B, 13(3), 409-415.

[55] Bowman, K. O., Lam, H. K. and Shenton, L. R. (1984), "Bounds for the Expectation of the kth Trot of a Random Variable," Journal of Computational and Applied Mathematics, Vol. 10, 229-244.

[56] Bowman, K.O., Lam, H. K. and Shenton, L. R. (1984), "Bounds for Certain Integrals," Journal of Computational and Applied Mathematics, Vol. 10, 245-254.

[57] Bowman, K. O. Lam, H. K. and Shenton, L. R. (1984), "Bounds for Integrals Using Segments," Journal of Computational and Applied Mathematics, Vol. 11, 57-67.

[58] Bowman, K. O., Shenton, L. R. and Szekeres, G. (1984), "A Poisson Sum up to the Mean and a Ramanujan Problem," Journal of Statistical Computation and Simulation, 20, 167-172.

[59] Bowman, K. O. and Shenton, L. R. (1985), "Methods of Moments," Encyclopedia of Statistical Sciences, Vol. 5, ed., Samuel Kotz and N. L. Johnson, John Wiley and Sons, Inc., 467-473.

[60] Bowman, K. O. and Shenton, L. R. (1985), "The Padé and sStiltjies Transformation," Encyclopedia of Statistical Sciences, Vol. 6, eds., Samuel Kotz and N. L. Johnson, 550-553.

[61] Kastenbaum, M. A. and Bowman, K. O. (1985), "Optimal Sample Size Requirement" Encyclopedia of Statistical Sciences, Vol. 6, ed., Samuel Kotz and N. L. Johnson, John Wiley and Sons, Inc., 445-449.

[62] Bowman, K. O., Shenton, L. R., and Bernard, C. R. (1985), "Study of Age Dependent Half-Life of Iodine in Man: A Reinforcement-Depletion Urn Model," Bull. Math. Biol., 47, 205-214.

[63] Bowman, K. O. and Shenton, L. R. (1985), "The Distribution of a Moment Estimator for a Parameter of the Generalized Poisson Distribution," Communications in Statistics, 14(4), 867-893.

[64] Shenton, L. R. and Bowman, K. O. (1985), "Factorial Series Distribution and Urn Model: Pseudo Convolution Property," Scandinavian Journal of Statistics Theory and Applications, 12(4), 293-299.

[65] Shenton, L. R. and Bowman, K. O. (1985), "The Continued Fraction for ln GAMMA(z): A Stiltjies Conjecture," Journal of Statistical Computation and Simulation, 23(1&2), 133-135.

[66] Bowman, K. O. and Shenton, L. R. (1986), "A Reinforcement-Depletion Urn Model: A Contiguity Case," Annals of the Institute of Statistical Mathematics, 38(2), 233-243.

[67] Bowman, K. O. and Shenton, L. R. (1986), "The Two-Color Urn Model: Recursions for the Moments," Commun. Statist. Computa., 15(3), 787-799.

[68] Bowman, K. O. and Shenton, L. R. (1986), "The Dark Side of Asymptotics and Moment Series," Sankhya A, 48(2). 219-231.

[69] Bowman, K. O., Lam, H. K. and Shenton, L. R. (1986), "Series for Student's Non-Central t under Exponential Sampling with Comments due to H.\0P.\0Mulholland," Commun. Statist. Simula. Computa., 15(3), 697-708.

[70] Bowman, K. O. and Shenton, L. R. (1987), "Sums of Powers of Binomial Coefficients," Commun. Statist. Simula. Computa., 16, 1189-1207.

[71] Bowman, K. O., Shenton, L. R. and H. K. Lam (1987), "Simulation and Estimation Problems Associated with the 3-Parameter Gamma Density", Commun. Statist. -Simula. Computa., 16, 1147-1188.

[72] Bowman, K. O. and Shenton, L. R. (1988), "Solutions to Johnson's SB and SU", Commun. Statist. -Simula. Computa., 17(2), 343-348.

[73] Bowman, K. O. and Shenton, L. R. (1989), "SB and SU Distributions fitted by Percentiles: A General Criterion", Commun. Statist. -Simula. Computa., 18(1), 1-13.

[74] Bowman, K. O. and Wallace, S. A. (1990), "Evaluation of Special Nuclear Material Monitoring Instruments", JNMM, XVIII, Number 2, 30-35.

[75] Bowman, K. O. and Shenton, L. R. (1990), "The Approximate Distribution of Four Moment Statistics from Type III Distribution", Commun. Statist. Theory & Methods, 19(4), 1511-1579.

[76] Bowman, K. O. and Shenton, L. R. (1992), "Parameter Estimation for the Beta Distribution", Journal of Statistical Computation and Simulation, 43, 217-228.

[77] Bowman, K. O. and Shenton, L. R. (1992), "Some Exact Expressions for Functions of Sample Moments", The Annals of the ISM,, 44(4), 781-798.

[78] Bowman, K. O, Hopp, T. H., Kacker, R. N. and Lundegard, R. J. (1991), "Statistical Quality Control Technology in Japan", Chance, 4(3), 15-21.

[79] Bowman, K. O., Kastenbaum, M. A. and Shenton, L. R. (1992), "The Negative Hypergeometric Distribution and Estimation by Moments", Commun. Statist. Simula-Computa.. 21(2), 301-332.

[80] Bowman, K. O. and Kastenbaum, M. A. (1992), "Overdispersion of Aggregated Genetics Data", Mutation Research, 272, 133-137.

[81] Nanstad, R.K., McCabe, D. E., Haggag, F. M., Bowman, K. O. and Downing, D. J. (1992), "Statistical Analyses of Fracture Toughness Results for Two Irradiated High-Copper Welds", Standard Technical Publication 1125, American Society for Testing and Materials.

[82] Bowman, K. O., Miller, M. K. and Shenton, L. R. (1993), "The use of moment estimators to determine the parameters of concentration fluctuations in random area atom probe analyses", Applied Surface Science, \f367, 424-428.

[83] Miller, M. K., Bowman, K. O., Cerezo, A. and Hyde, J. K. (1993), "Comparison of models for deconvoluting the compositions of coexisting phases", Applied Surface Science, \f367, 429-435.

[84] Bowman, K. O., Miller, M. K. and Shenton, L. R. (1994), "The evaluation of moments methods for fitting multiparameter sinusoidal models", Applied Surface Science, 76/77, 403-408.

[85] Bowman, K. O. and Shenton, L. R. (1994), Additional Bowman-Shenton Approximate Percentage Points for Pearson Distributions Based on Pearson Type VI, Commun. Statist. Simula-Computa., 23(3), 583-590.

[86] Bowman, K. O. and Shenton, L. R. (1995), Contribution to the discussion on the paper by R. C. H. Cheng and L. Taylor on "Non-regular Maximum Likelihood Problems" on 19 January, 1995, JRSS, 57(1), 34-35.

[87] Bowman, K. O., Shenton, L. R. and Karlof, C. (1995), Estimation Problems Associated with the Three Parameter Gamma Distribution, Commun. Statist. Theory Meth., 24(5), 1355-1376.

[88] Shenton, L. R. and Bowman, K. O. (1996), Moment Solution to an Urn Model, AISM, 48(1), 169-184.

[89] Bowman, K. O., Kastenbaum, M. A. and Shenton, L. R. (1996), Fitting Multi-Parameter Distributions to SCE Data, Mutation Research, 358, 15-24.

[91] Shenton, L. R. and Bowman, K. O. (1997). Replenishment-Depletion: Urn in Equilibrium, AISM, 49(4), 749-760.

[92] Bowman, K. O. and Shenton, L. R. (1997). The Cornish-Fisher Expansion for Estimating Percentage Points: A Numerical Perspective, Commun. Statist. Simula-Comuta, 26(1), 355-373.

[93] Bowman, K. O. and Shenton, L. R. (1997). The Gamma Distribution, Encyclopedia of Biostatistics, John Wiley and Sons, New York.

[94] Bowman, K. O., Shenton, L. R. and Gailey, P.C, (1998). Distribution of ratio of Gamma variate, Commun. Statist. Simula-Comuta, 27(1), 1-19.

[95] Bowman, K.O., Eddings, W., Kastenbaum, M.A., and Shenton, L.R. (1998), Sister chromatid exchange data and Gram-Charlier series, Mutation Research, 403, 159-169.

[96] Bowman, K.O. and Shenton, L. R. (1998). Asymptotic Skewness and the Distribution of Maximum Likelihood Estimators, Commun. Statist. Theory and Method, 27(11), 2743-2760.

[97] Bowman, K.O. and Shenton, L.R. (1999). The Asymptotic Kurtosis for Maximum Likelihood Estimators, Commun. Statist. Theory and Method, 28(11),2641-2654.

[98] Bowman, K.O. and Shenton, L.R. (1999). The Asymptotic Moment Profile and Maximum Likelihood: Applications to Gamma and Gamma Ratio Densities, Commun. Statist. Theory and Method, 28(10), 2497-2508.

[99] Bowman, K.O. and Shenton, L.R. (2000). Maximum Likelihood and the Weibull Distributions, Far East Journal of Theoretical Statistics, 4(2), 391-422.

[100] Bowman, K.O. and Shenton, L.R. (2001). Weibull Distributions when the Shape Parameter is Defined, Computational Statistics and Data Analysis , 36, 299-310.

[100] Williams, P.T., Bowman, K.O., Bass, B.R., and Dickson, T.L. (2001). Weibull Statistical Models of K(Ic)/K(Ia) Fracture Toughness Databases for Pressure Vessel Steels with an Application to Presdutized Thermal Shock Assessments of nuclear Reactor Pressure Vessels, International Journal of Pressure Vessels and Piping, 78,165-178.

[101] Shenton, L.R. and Bowman, K.O. (2001). The Geometric Distribution, Cumulants, Eulerian Numbers, and the Logarithmic Function, Far East Journal of Theoretical Statistics , 5(1). 113-142.

[102] Bowman, K.O. and Shenton, L.R. (2002). Problems with Maximum Likelihood Estimations and the 3 Parameter Gamma Distribution, J. Statistical Computation and Simulation , 72(5),391-401.

[103] Shenton, L. R. and Bowman, K. O. (2002), The Geometric distribution's Central Moments and Eulerian Numbers of the Second Kind, Far East Journal of Theoretical Statistics, 7(1), 1-17.

[104] Bowman, K. O. and Shenton, L. R. (2002), Poisson Mixture of k Components, Far East Journal of Theoretical Statistics , 7(2), 93-110.

[105] Bowman, K. O. and Shenton, L. R. (2003), Sample size assessment and the two component Poisson mixture, proportion known, Far East Journal of Theoretical Statistics, 9(2), 97-115.

[106] Bowman, K. O. and Shenton, L. R. (2003), Canonical dichotomized alternant determinants and Poisson mixtures, Far East Journal of Theoretical Statistics , 10(2),87-109.

[107] Bowman, K. O. and Shenton, L. R. (2004), Mixtures, hybrid mixtures, canonical forms, and Matusita's distance, Far East Journal of Theoretical Statistics, 12(1), 69-88.

[108] Bowman, K. O. and Shenton, L. R. (2004), Poisson mixtures, asymptotic variance, and alternant determinants, Far East Journal of Theoretical Statistics, 14(1), 79-87.

[109] Bowman, K. O. and Shenton, L.R, (2005), The asymptotic variance and skewness of maximum likelihood estimators using Maple, Journal of Statistical Computation and Simulation, 75(12), 975-986.

[110] Shenton, L. R. and Bowman, K. O. (2005), Roger's continued fractions: New properties, Far East Journal of Theoretical Statistics, 18(1), 1-11.

[111] Shenton, L. R. and Bowman, K. O. (2005), Polygamma functions, the zeta functions, and Euler numbers. Far East Journal of Applied Mathematics, 18(3), 241-249.

[112] Shenton, L.R. and Bowman, K.O. (2005), Second order continued fractions and Fibonacci numbers, Far East Journal of Applied Mathematics, 20(1), 17-31.

[113] Bowman, K.O. and Shenton, L.R. (2005), Bias, Variance, Skewness and Kurtosis of Maximum Likelihood Estimators using Maple, Far East Journal of Theoretical Statistics, 17(2), 137-195.

[114] Bowman, K.O. and Shenton, L.R. (2006), Moments of Maximum Likelihood Estimators in the Discrete Case, Far East Journal of Theoretical Statistics, 18(1), 61-91.

[115] Bowman, K.O. and Shenton, L.R. (2006), Binomial and Poisson mixtures, maximum likelihood, and Maple code, Far East Journal of Theoretical Statistics, 20(1), 73-95.

[116] Bowman, K.O. and Shenton, L.R. (2006), Maximum likelihood estimators for normal and gamma mixtures, Far East Journal of Theoretical Statistics, 20(2), 217-240.

[117] Bowman, K.O. and Shenton, L.R. (2007), Skewness for maximum likelihood estimators for the negative binomial distribution, Far East Journal of Theoretical Statistics, 22(1), 103-129.

[118] Bowman, K.O. and Shenton, L.R. (2007), Binomial test statistics using Psi functions, Far East Journal of Theoretical Statistics, 23(1), 103-117.

[119] Bowman, K.O. and Shenton, L.R. (2007), The beta distribution, moment method, Karl Pearson and R.A. Fisher, Far East Journal of Theoretical Statistics, 23(2), 133-165.

[119] Bowman, K.O. and Shenton, L.R. (2007), Mixture distributions and a test statistic, Far East Journal of Theoretical Statistics, 23(2), 241-259.

[120] Shenton, L.R. and Bowman, K.O. (2008), Montage for the gamma functions, Far East Journal of Applied Mathematics, 32(1), 1-11.

[121] Shenton, L.R. and Bowman, K.O. (2008), Zeros and Stieltjes continued fraction for $J(z)$, Far East Journal of Theoreticcal Statistics, 26(1), 83-95.

[122] Shenton, L.R. and Bowman, K.O. (2009), The derivative of a continued fraction, Far East Journal of Appled Mathematics, 35(3), 363-371.

[123] Bowman, K.O. and Shenton, L.R. (2009), The Pearson and Hansmann Manifolds for Statistical Distributions, Far East Journal of Theoreticcal Statistics, 29(2), 157-173.

[124] Bowman, K.O. and Shenton, L.R. (2010), Definite integrals, some involving residue theory, evaluated by the Maple code, Far East Journal of Theoretical Statistics , 31(2), 107-116.

[125] Bowman, K.O. and Shenton, L.R. (2010), A Fascinating series due to Stieltjes, Far East Journal of Applied Mathematics , 43(1),57-63.

[126] Bowman, K.O. and Shenton, L.R. (2011), A montage for the binomial distribution Stieltjes transform, Far East Journal of Theoretical Statistics , 34(2),123-127.

Newsletter Articles

[1] Bowman, K. O. (1977), "Japanese Government Statistical activities," Scientific Bulletin ONR, 2(3), 57-60.

[2] Bowman, K. O. (1977), "National Research Institute for Metals," Scientific Bulletin ONR, 2(4) 64-65.

[3] Bowman, K. O. (1977), "Some Quality Control Activity in Japan," Scientific Bulletin ONR, 2(3), 61-65.

[4] Bowman, K. O. (1977) "Statistics Research at Chiba University," Scientific Bulletin ONR, 2(4), 67-68.

[5] Bowman, K. O. (1978), "Statistical Research in Japan," Scientific Bulletin ONR, 3(1), 63-74.

[6] Bowman, K. O. (1985), "Progress Report on Japanese Computer Projects," Scientific Bulletin, 10(1), ONRFE/AFOSRFE, 91-110.

[7] Bowman, K. O. (1985), "The Laboratory for Gastrointerology at Gumma University," Scientific Bulletin, 10(1), ONRFE/AFOSRFE, 111-112.

[8] Bowman, K. O. (1985), "Machine Translation Research at Kyoto University," Scientific Bulletin, 10(2), ONRFE/AFOSRFE, 1-3.

[9] Bowman, K. O. (1986), "Total Quality Control at the Kansai Electric Power Company," Scientific Bulletin, 11(1), ONRFE/AFOSRFE,19-32.

[10] Bowman, K. O., Hopp, T. H., Kacker, R. N. and Lundegard, R. J. (1990), "Statistical Quality Control technology in Japan", Scientific Information Bulletin, 15(1), ONRFE/AFOSRFE/AROFE, 57-73.

Proceedings:

[1] Bowman, K. O. and Shenton, L. R. (1969), "Remarks on Maximum Likelihood Estimators for the Gamma Distribution," Proc. ICQC, Tokyo, 519-522.

[2] Bowman, K. O. and Shenton, L. R. (1971), "Remarks on the Distribution of the Skewness Statistic sqrt(b1) in Sampling from Normal Type A Distributions," Proc. of the 38th Session of the Internat. Statist. Inst., Washington, DC, 57- 63.

[3] Bowman, K. O. and Shenton, L. R. (1971), "Remarks on the Distribution of the Skewness Statistic sqrt(b1) in Sampling from Normal Type A Distributions," Bull. Internat. Statist. Inst. Proc. of the 38th Session, Vol. XLIV, Book 2, 115-121.

[4] Bowman, K. O. and Shenton, L. R. (1973), "Remarks on the Distribution of Karl Pearson's k-Statistic, k = 2b2 - 3b1 - 6," Proc. of the 39th Session of the Statist. Inst., Vol. 1, Vienna, Austria, 134-142.

[5] Shenton, L. R. and Bowman, K. O. (1973), "Comments on the Gamma Distribution and Uses in Rainfall Data," Proc. of 3rd Conf. on Prob. and Stat. in Atmospheric Science, Boulder, CO, June 19-22.

[6] Shenton, L. R. and Bowman, K. O. (1973), "Comments on Higher Order Terms in Moment of Moments, Moments of Maximum Likelihood Estimators, Regression Residuals, Proc. of Internat. Conf. on Asymptotic Methods of Stat. and Their Appl. on Physical and Social Science, IASPS.

[7] Shenton, L. R. and Bowman, K. O. (1974), "Comments on Higher Order Terms in Moment of Moments, Moments of Maximum Likelihood Estimators, Regression Residuals," Proc. of the Prague Symposium on Asymptotic Statistics, September 3-6, 1973., Vol. 2, ed., Jaroslan Jajek, Charles University, Prague, 323-344.

[8] Bowman, K. O. and Shenton, L. R. (1975), "Comments on the Distribution of the Variance in Sampling from the Logistic Distribution," Proc. of the 40th Session of ISI, Warsaw.

[9] Bowman, K. O. and Shenton, L. R. (1975), "Remarks on the Distribution of the Skewness and Kurtosis Statistics," Proc. of the 1st ERDA Statist. Symposium, 104-124.

[10] Bowman, K. O. and Shenton, L. R. (1976), "Summing Asymptotic Series," Proceedings of the American Statistical Association, Statistical Computing Section, 121-125.

[11] Bowman, K. O., Beauchamp, J. J. and Shenton, L. R. (1977), "Error Contours for Student's t Under Non-Normality ," Proceedings of the American Statistical Association, Statistical Computing Section, 133-137.

[12] Bowman, K. O., Lam, H. K. and Shenton, L. R. (1978), "Characteristics of Moment Series for Student's t and Other Statistics in Non-Normal Sampling," Proceedings of the American Statistical Association, Statistical Computing Section, 206-211.

[13] Bowman, K. O. and Shenton, L. R. (1978), "Coefficient of Variation on Sampling from a Gamma Universe," Proceedings of the International Conference on Quality Control, 1978-Tokyo, D1-19--D1-24.

[14] Shenton, L. R., Bowman, K. O. and Lam, H. K. (1979), "Problems Associated with Approximating Distributions," Proceedings of the American Statistical Association, Statistical Computing Section, invited paper, 20-29.

[15] Lam, H. K., Bowman, K. O. and Shenton, L. R. (1980), "Remarks on the Generalized Tukey's Lambda Family of Distribution," Proceedings of the American Statistical Association, Statistical Computing Section, Washington, DC, 134-139.

[16] Bowman, K. O. and Shenton, L. R. (1981), "Moment Series for the Coefficient of Variation in Weibull Sampling," Proceedings of the American Statistical Association, Statistical Computing Section, Washington, DC, 148-153.

[17] Lam, H. K., Bowman, K. O. and Shenton, L. R. (1981), "The Transformed Beta Distribution and Its Application in Distribution Fitting," Proceedings of the American Statistical Association, Statistical Computing Section, Washington, DC, 111-116.

[18] Bowman, K. O. and Shenton, L. R. (1983), "Moment Series for Moment Estimators of the Parameters of a Weibull Density," Proceedings of Computer Science and Statistics: 14th Symposium on the Interface, Springer-Verlag, New York, 174-186.

[19] Bowman, K. O. and Mark T. Robinson (1987), Studies of Random Number Generators for Parallel Processing, Hypercube Multiprocessor 1987, ed by M. T. Heath, SIAM, 45-453.

[20] Lam, H. K., Shenton, L. R. and Bowman, K. O. (1988), Some Properties of a Moment Estimator for the Index Parameter of the Negative Binomial Distribution, Proceedings of the American Statistical Association, Statistical Computing Section, Washington, DC.

Books and Book Chapter:

[1] Bowman, K. O., Hutcheson, K., Odum, E. P. and Shenton, L. R. (1971), "Comments on the Distribution of Indices or Diversity," Statist. Ecol., Vol. 3: Many Species Populations, Ecosystems, and Systems Anal., ed., G. P. Patil, E. C. Pielow and W. E. Waters, Pennsylvania State University Press, 315-366.

[2] Bowman, K. O. and Dusenberry, W. E. (1975), "Transformation of the Pearson System with Special Reference to Type IV," A Modern Course on Statistical Distributions on Scientific Work, Vol.\01:\0\0Models and Structures, ed., G. P. Patil, S. Kotz and J. K. Ord, Reidel Publishing Co., 381-390.

[3] Bowman, K. O. and Kastenbaum, M. A. (1975), "Sample Size Requirement: Single and Double Classification Experiments, Selected Tables in Mathematical Statistics," American Mathematical Society and Institute of Mathematical Statistics, ed., D. B. Owen and H. L. Harter, 111-232.

[4] Shenton, L. R. and Bowman, K. O. (1977), Maximum Likelihood Estimation in Small Samples, England: Charles Griffin and Co., Ltd.

[5] Bowman, K. O. and Shenton, L. R. (1986), "Moment (sqrt(b1), b2) Techniques," Handbook of Goodness of Fit Techniques, ed., R.B. D'Agostino and M. Stephens, Marcel Dekker, Inc., 277-327.

[6] Bowman, K. O. and Robinson, M. T. (1987), "Studies of Random Number Generators for Parallel Processing", Hypercube Multiprocessors 1987, M. T. Head (ed), SIAM., 445-453.

[7] Bowman, K. O. and Shenton, L. R. (1987), "Power Transformation of the Sample Kurtosis", Proceedings of the 46th Session of the International Statistical Institute.

[8] Bowman, K. O. (1987), "Statistical Inference - Computer Algorithmic Approach", Proceedings of the First IASC World Conference on Computational Statistics and Data Analysis.

[9] Bowman, K. O. and Shenton, L. R. (1988), Properties of Estimators for the Gamma Distribution, Marcel Dekker, Inc.

[10] Bowman, K. O. and Shenton, L. R. (1989), Continued Fractions in Statistical Applications, Marcel Dekker, Inc.

[11] Bowman, K. O. (1998). "Statistics and My Life", She does Statistics, edted by Martha Aliaga, Mathematical Association of America.