On zero - inflated logarithmic series distribution and its modification

Authors

  • C. Satheesh Kumar University of Kerala
  • A. Riyaz University of Kerala

DOI:

https://doi.org/10.6092/issn.1973-2201/4498

Abstract

Here we consider a zero-inflated logarithmic series distribution (ZILSD) and study some of its properties. A modified form of ZILSD is also developed and derived several important aspects of it. The parameters of modified ZILSD are estimated by method of maximum likelihood and illustrated the procedure using certain real life data sets. Further, certain test procedures are suggested.

References

C. CHATFIELD, A. S. C. EHRENBERG, G. J. GOODHARDT (1966). Progress on a simplified model of Stationary purchasing behavior (with discussion). Journal of the Royal Statistical Society, Series A, 129, pp. 317-367.

C. CHATFIELD (1986). Discrete distributions and purchasing models. Communication in Statistics-Theory and Methods, 15, pp. 697-708.

J. B. DOUGLAS (1980). Analysis with standard contagious distribution. Statistical distributions in scientific work (ed. G. P. Patil), International cooperative publishing house, Fairland, pp. 241-262.

R. A. FISHER, A. S. CORBERT, C.B. WILLIAMS (1943).The relation between the number of species and the number of individuals in a random sample of an animal population. Journal of Animal Ecology, 12, pp. 42-58.

M. GREENWOOD, G. U. YULE (1920). An inquiry into the nature of frequency distributions representative of multiple happenings with particular reference to the occurrence of multiple attacks of disease or of repeated accidents. Journal of Royal Statistical Society, 83, pp. 255-279.

G. C. JAIN, R. P. GUPTA (1973). A logarithmic series type distribution. Trabaios de Estadistica, 24, pp.99- 105.

N. L. JOHNSON, A. W. KEMP, A. W. KOTZ (2005). Univariate Discrete Distributions. Wiley, New York.

T. F. KANG, S. H. ONG (2007). A new generalization of the logarithmic distribution arising from the inverse trinomial distribution. Communication in Statistics–Theory and Methods, 36, pp. 3 – 21.

R. A. KEMPTON (1975). A generalized form Fisher’s logarithmic series. Biometrika, 62, pp. 29-38.

C. S. KUMAR (2009). Some properties of Kemp family of distributions. Statistica, 69, pp. 311-316.

A. M. MATHAI, H. J. HAUBOLD (2008). Special Functions for Applied Scientists. Springer, New York.

S. H. ONG (2000). On a generalization of the log-series distribution. Journal of Applied Statistical Science, 10(1), PP. 77- 88.

P. PUIG (2003). Characterizing additively closed discrete models by a property of their MLEs, with an application to generalized Hermite distribution. Journal of American Statistical Association, 98, pp. 687-692.

C. R. RAO (1973). Linear Statistical Inference and its Applications. John Wiley, New York.

L. J. SLATER (1966). Generalized Hypergeometric Functions. Cambridge university press, Cambridge.

R. C. TRIPATHI, R. C. GUPTA (1985). A generalization of the log-series distribution. Communication in Theory and Methods, 14, pp. 1779-1799.

R. C. TRIPATHI, R. C. GUPTA (1988). Another generalization of the logarithmic series and the geometric distribution. Communication in Statistics-Theory and Methods, 17, pp. 1541-1547.

Downloads

Published

2013-12-30

How to Cite

Kumar, C. S., & Riyaz, A. (2013). On zero - inflated logarithmic series distribution and its modification. Statistica, 73(4), 477–492. https://doi.org/10.6092/issn.1973-2201/4498

Issue

Section

Articles