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首页> 外文期刊>Journal of King Saud University >A bounded distribution derived from the shifted Gompertz law
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A bounded distribution derived from the shifted Gompertz law

机译：从偏移的Gompertz定律导出的有界分布

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摘要

A two-parameter probability distribution with bounded support is derived from the shifted Gompertz distribution. It is shown that this model corresponds to the distribution of the minimum of a random number with shifted Poisson distribution of independent random variables having a common power function distribution. Some statistical properties are written in closed form, such as the moments and the quantile function. To this end, the incomplete gamma function and the LambertWfunction play a central role. The shape of the failure rate function and the mean residual life are studied. Analytical expressions are also provided for the moments of the order statistics and the limit behavior of the extreme order statistics is established. Moreover, the members of the new family of distributions can be ordered in terms of the hazard rate order. The parameter estimation is carried out by the methods of maximum likelihood, least squares, weighted least squares and quantile least squares. The performance of these methods is assessed by means of a Monte Carlo simulation study. Two real data sets are used to illustrate the usefulness of the proposed distribution.
机译：从偏移的Gompertz分布中导出具有有限支持的两参数概率分布。结果表明，该模型对应于具有公共幂函数分布的独立随机变量的移位泊松分布的随机数最小值分布。一些统计属性以封闭形式编写，例如矩和分位数函数。为此，不完整的伽马函数和LambertW函数起着核心作用。研究了故障率函数的形状和平均剩余寿命。还提供阶次统计信息的分析表达式，并建立了极限阶次统计信息的极限行为。而且，可以根据危险率顺序来订购新的分布系列的成员。通过最大似然，最小二乘，加权最小二乘和分位数最小二乘的方法来进行参数估计。这些方法的性能通过蒙特卡洛模拟研究进行评估。使用两个实际数据集来说明所建议的分布的有用性。

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