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Keywords:
misclassification; size-biased modified power series distribution; raw moments; central moments; factorial moments; variance ratio; inverted parabola; generalized Poisson; generalized negative binomial
misclassification; size-biased modified power series distribution; raw moments; central moments; factorial moments; variance ratio; inverted parabola; generalized Poisson; generalized negative binomial
Summary:
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 $\alpha $, 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.
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