Approximate MLEs for the location and scale parameters of the Poisson-half-logistic distribution

IF 1.1 Q3 STATISTICS & PROBABILITY
M. Niaparast, Leila Esmaeili
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引用次数: 0

Abstract

Recently, the application of compound distributions has increased due to the flexibility in fitting to actual data in various fields such as economics, insurance, etc. Poisson-half-logistic distribution is one of these distributions with an increasing-constant hazard rate that can be used in parallel systems and complementary risk models. Because of the complexity of the form of this distribution, it is not possible to obtain classical parameter estimates (such as MLE) by the analytical method for the location and scale parameters. We present a simple way of deriving explicit estimators by approximating the likelihood equations appropriately. This paper presents AMLE (Approximate MLE) method to obtain the location and scale parameters estimation. Using simulation, we show that this method is as efficient as the maximum likelihood estimators (MLEs), we obtain the variance of estimators from the inverse of the observed Fisher information matrix, and we see that when sample size increases bias and variance of these estimators, MSEs of parameters decrease. Finally, we present a numerical example to illustrate the methods of inference developed here.
泊松半逻辑分布的位置和尺度参数的近似MLE
最近,由于在经济、保险等各个领域能够灵活地拟合实际数据,复合分布的应用有所增加。泊松半逻辑分布是其中一种具有不断增加的恒定危险率的分布,可用于并行系统和互补风险模型。由于这种分布形式的复杂性,不可能通过位置和尺度参数的分析方法获得经典的参数估计(如MLE)。我们提出了一种通过适当地逼近似然方程来导出显式估计量的简单方法。本文提出了AMLE(近似MLE)方法来获得位置和尺度参数的估计。通过仿真,我们证明了该方法与最大似然估计量(MLE)一样有效,我们从观测到的Fisher信息矩阵的逆中获得了估计量的方差,并且我们看到当样本大小增加这些估计量的偏差和方差时,参数的MSE减小。最后,我们给出了一个数值例子来说明这里发展的推理方法。
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来源期刊
CiteScore
3.30
自引率
26.70%
发文量
53
期刊介绍: Pakistan Journal of Statistics and Operation Research. PJSOR is a peer-reviewed journal, published four times a year. PJSOR publishes refereed research articles and studies that describe the latest research and developments in the area of statistics, operation research and actuarial statistics.
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