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Misclassified size-biased modified power series distribution and its applications. (English) Zbl 1206.62010
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 particular cases, like size-biased generalized negative binomial (SBGNB) and 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 distributions. 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.
##### MSC:
 62E15 Exact distribution theory in statistics 62E10 Characterization and structure theory of statistical distributions 62F03 Parametric hypothesis testing
##### Keywords:
raw moments; central moments
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