一种新的离散分布:性质、表征、实数数据建模、贝叶斯和非贝叶斯估计

IF 1.6 Q1 STATISTICS & PROBABILITY Statistica Pub Date : 2021-10-26 DOI:10.6092/ISSN.1973-2201/11635
H. Yousof, C. Chesneau, G. Hamedani, M. Ibrahim
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引用次数: 11

摘要

本文定义并研究了一种新的离散分布,其中包括离散Burr-Hatke分布。导出了相关的统计性质。新分布的概率质量函数可以是不同形状的“右偏斜”、双峰和“均匀”分布。相应的风险率函数可以是“单调递减”、“倒挂递增”、“倒挂递增”、“倒挂递增”、“倒挂递增”。给出了均值、方差、偏度、峰度和离散度指数的数值分析。新的分布可以用于“欠分散”或“过度分散”计数数据的建模。提出了新分布的某些特征。这些特征是基于随机变量的某个函数的条件期望和风险率函数。考虑了贝叶斯和非贝叶斯估计方法。对贝叶斯估计方法和非贝叶斯估计方法进行了数值模拟比较。将该模型应用于龋齿数据和肾囊肿计数数据的建模。
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A New Discrete Distribution: Properties, Characterizations, Modeling Real Count Data, Bayesian and Non-Bayesian Estimations
In this work, a new discrete distribution which includes the discrete Burr-Hatke distribution is defined and studied. Relevant statistical properties are derived. The probability mass function of the new distribution can be "right skewed" with different shapes, bimodal and "uniformed". Also, the corresponding hazard rate function can be "monotonically decreasing", "upside down", "monotonically increasing", "upside down increasing", and "upside down-constant-increasing". A numerical analysis for the mean, variance, skewness, kurtosis and the index of dispersion is presented. The new distribution could be useful in the modeling of "under-dispersed" or "overdispersed" count data. Certain characterizations of the new distribution are presented. These characterizations are based on the conditional expectation of a certain function of the random variable and in terms of the hazard rate function. Bayesian and non-Bayesian estimation methods are considered. Numerical simulations for comparing Bayesian and non-Bayesian estimation methods are performed. The new model is applied for modeling carious teeth data and counts of cysts of kidneys data.
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来源期刊
Statistica
Statistica STATISTICS & PROBABILITY-
CiteScore
1.70
自引率
0.00%
发文量
0
审稿时长
10 weeks
期刊最新文献
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