New class of location-parameter discrete probability distributions and their characterizations. (English) Zbl 0728.62017
Summary: A new class of location-parameter discrete probability distributions (LDPD) has been defined where the population mean is the location parameter. It has been shown that some single parameter discrete distributions do not belong to this class and all discrete probability distributions belonging to this class can be characterized by their variances only. Expressions are given for the first four central moments and a recurrence formula for higher central moments has been obtained. Eight theorems are given to characterize the various distributions in the LDPD class.
MSC:
| 62E10 | Characterization and structure theory of statistical distributions |
Keywords:
power-series distributions; modified power series distributions; characterizations; generalized Poisson; negative binomial distributions; location-parameter discrete probability distributions; population mean; variances; recurrence formula; higher central moments; LDPD classReferences:
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