• SOME PROPERTIES AND APPLICATION OF SIZE-BIASED POISSON-LINDLEY DISTRIBUTION

Abstract

Size-biased distributions are a special case of the more general form known as weighted distributions. Such distributions arise naturally in practice when observations from a sample are recorded with unequal probability. In this study, size-biased Poisson-Lindley distribution (SBPL) is further investigated by working out recursive relationship of the probabilities, moments and cumulants etc. Some distributional properties of size-biased Poisson-Lindley distribution including moments, cumulants, harmonic mean, coefficient of variation, reliability function etc has been derived. The estimate of the parameter is obtained by employing method of moments and ratio of the first two relative frequencies. To justify the suitability, the distribution is fitted to a number of reported data sets. The resulting fit is found to be good in comparison to others.