An Intervened Poisson Distribution and Its Medical Application

Abstract

Among probability distributions that are used to describe a chance mechanism whose observational apparatus becomes active only when at least one event occurs is the zero-truncated Poisson distribution (ZTPD). A modified version of the ZTPD, which we call an intervened Poisson distribution (IPD), is discussed in this paper. We give a genesis of IPD and obtain its statistical properties. A numerical example is included to illustrate the results.

On Finite Mixtures of Modified Intervened Poisson Distribution And Its Applications

“…Shanmugam [8] obtained the distribution of U and its statistical properties, and gave an example to illustrate its application. The probability mass function ( pmf) of the IPD is given by…”

“…The IPD has been found applications in several areas of research such as reliability analysis, queuing problems, epidemiological studies etc. For example, see Huang and Fung [3] and Shanmugam [8,9]. During the observational period, the failed units are either replaced by new units or rebuilt.…”

Compound Intervened Poisson Distribution

“…Applying the recurrence relation for generalized Stirling number of second kind (Shanmugam (1984)), namely Sk 1Y nY l n À l SkY nY l SkY n À 1Y l, to (15) gives…”

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SummaryThe nature and characteristics of Intervened Poisson Distribution (IPD) has been well discussed by Shanmugam (1985). In this paper, Compound Intervened Poisson Distribution (CIPD) is introduced and its properties are studied.

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“…Introduction Shanmugam (1985) has introduced Intervened Poisson Distribution (IPD) and studied its general characteristics. He also discussed the inferential problems like unbiasedness, sufficiency, complete sufficiency and MVUE.…”