The Reflected-Shifted-Truncated Lindley Distribution with Applications

Q3 Mathematics Stochastics and Quality Control Pub Date : 2020-11-10 DOI:10.1515/eqc-2020-0008
S. Dey, Sophia D. Waymyers, D. Kumar
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引用次数: 1

Abstract

Abstract In this paper, a new probability density function with bounded domain is presented. The new distribution arises from the Lindley distribution proposed in 1958. It presents the advantage of not including any special function in its formulation. The new transformed model, called the reflected-shifted-truncated Lindley distribution can be used to model left-skewed data. We provide a comprehensive treatment of general mathematical and statistical properties of this distribution. We estimate the model parameters by maximum likelihood methods based on complete and right-censored data. To assess the performance and consistency of the maximum likelihood estimators, we conduct a simulation study with varying sample sizes. Finally, we use the distribution to model left-skewed survival and failure data from two real data sets. For the real data sets containing complete data and right-censored data, this distribution is superior in its ability to sufficiently model the data as compared to the power Lindley, exponentiated power Lindley, generalized inverse Lindley, generalized weighted Lindley and the well-known Gompertz distributions.
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反射偏移截断林德利分布及其应用
摘要本文提出了一种新的有界域概率密度函数。新的分布源于1958年提出的林德利分布。它的优点是在公式中不包含任何特殊函数。新的转换模型,称为反射移位截断林德利分布,可用于左偏数据建模。我们对这种分布的一般数学和统计性质进行了全面的处理。我们基于完整和右截尾数据用最大似然方法估计模型参数。为了评估最大似然估计器的性能和一致性,我们进行了不同样本量的模拟研究。最后,我们使用该分布对来自两个真实数据集的左偏生存和失效数据进行建模。对于包含完整数据和右截尾数据的真实数据集,与幂林德利分布、幂林德利分布、广义逆林德利分布、广义加权林德利分布和著名的Gompertz分布相比,该分布在充分建模数据方面具有优势。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Stochastics and Quality Control
Stochastics and Quality Control Mathematics-Discrete Mathematics and Combinatorics
CiteScore
1.10
自引率
0.00%
发文量
12
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