Generalizing Sample Size of Normally Distributed Samples using Generalized Exponential Power Distribution

There are various sample size estimation formulas that are published in literature but has no adequate mathematical and statistical background. Many of such formula often assumed normal distribution that becomes unreliable most especially when observations are few. This study thus, established sample size estimation formula from generalized exponential power distribution (GEPD) which has normal, Laplace and uniform distribution has its members. We employed an approximation to the incomplete gamma cumulative distribution function of the GEPD via series expansion to obtain the pivotal quantity from which the sample size of GEPD was derived. Application to sample size calculation from Likert scaled questionnaire was demonstrated.

Gadbury, G.L., Page, G.P., Edwards, J., Kayo, T. Prolla, T.A., Weindruch, R., Permana P.A., Mountz, J.D., and Allison, D.B. (2004). Power and sample size estimation in high dimensional biology. Statistical Methods in Medical Research, 13:325-338.

 

Gomez, E., Gomez-Villegas, M.A., and Martin, J.M. (1998). A multivariate generalization of the exponential power family of distributions. Communications in Statistics A27: 589-600.

 

Johnson, R.A. and Wichern, D.W. (2006). Applied Multivariate Statistical Analysis. Englewood Clis, NJ: Prentice-Hall, Inc.

 

Jung, S.H., Chow, S.C., and Chi, E.M. (2007). On sample size calculation based on propensity analysis in non-randomized trials. Journal of Biopharmaceutical Statistics, 17:35-41.

 

Lindsey J.K. (1999). Multivariate elliptically contoured distributions for repeated measurements. Biometrics 55: 1277 -1280.

 

Mood, A. M., Graybill, F. A. and Boes, D. C. (1974). Introduction to the Theory of Statistics (McGraw-Hi1l Series in Probability and Statistics). ISBN 0-07-042864-6.

 

Nadarajah, S. (2005). A generalized normal distribution. Journal of Applied Statistics 32(7): 685-694. DOI:10.1080/02664760500079464.

 

Paris, R.B. (2010). Incomplete Gamma Function. NIST Handbook of Mathematical Functions, Cambridge University press.

Stacy, E.W. (1962). A generalization of the gamma distribution. Annals of Mathematical Statistics, 33(3): 1187-1192.

 

Suhasini, S.R. (2010). Advanced Statistical Inference. suhasini.subbarao@stat.tamu.edu.

 

Takenaga, R. (1966). On the Evaluation of the Incomplete Gamma Function. Math.Comp., 20 (96): 606-610.

 

Winitzki, S. (2003). Computing the incomplete gamma function to arbitrary precision. Lecture Notes Comp. Sci. 2667: 790-798.

 

Zacks, S. (1981). Parametric Statistical Inference Basic Theory and Modern Approaches. Pergamon Press State University of New York Binghamton.