Anwar Hassan, P. G. Department of Statistics, University of Kashmir, Srinagar, India, e-mail: anwar.hassan2007@gmail.com, anwar$_-$hassan2007@hotmail.
com; Peer Bilal Ahmad, P. G. Department of Statistics, University of Kashmir, Srinagar, India, e-mail: peerbilal@yahoo.co.in
Abstract: A misclassified size-biased modified power series distribution (MSBMPSD) where some of the observations corresponding to $x = 2$ are misclassified as $x = 1$ with probability $\al$, is defined. We obtain its recurrence relations among ordinary, central and factorial moments and also for some of its particular cases like the size-biased generalized negative binomial (SBGNB) and the size-biased generalized Poisson (SBGP) distributions. We also discuss the effect of the misclassification on the variance for MSBMPSD and illustrate an example for size-biased generalized negative binomial distribution. Finally, an example is presented for the size-biased generalized Poisson distribution to illustrate the results, and a goodness of fit test is also done using the method of moments.
Keywords: misclassification, size-biased modified power series distribution, raw moments, central moments, factorial moments, variance ratio, inverted parabola, generalized Poisson, generalized negative binomial
Classification (MSC 2000): 62E15, 62E10, 60E05
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