Abstract

In this article, we have considered the estimation of the probability density function and cumulative distribution function of the one-parameter polynomial exponential family of distributions. A number of probability distributions like the exponential, Lindley, length-biased Lindley and Sujatha are particular cases. Two estimators—maximum likelihood and uniformly minimum variance unbiased estimators of the probability density function and cumulative distribution function of the family have been discussed. The estimation issues of the length-biased Lindley and Sujatha distribution have been considered in detail. The estimators have been compared in mean squared error sense. Monte Carlo simulations and real data analysis are performed to compare the performances of the proposed estimators.

摘要

在本文中，我们考虑了单参数多​​项式指数分布族的概率密度函数和累积分布函数的估计。许多概率分布，如指数分布、林德利分布、长度偏向林德利分布和 Sujatha 分布都是特例。已经讨论了家庭的概率密度函数和累积分布函数的两个估计量——最大似然和一致最小方差无偏估计量。详细考虑了长度偏差 Lindley 和 Sujatha 分布的估计问题。估计量已在均方误差意义上进行了比较。执行蒙特卡罗模拟和实际数据分析以比较所提出的估计器的性能。