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Reliability functions of generalized log-normal model

机译:广义对数正态模型的可靠性函数

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摘要

It is well known that in many practical applications, the data follow a log-normal distribution instead of a normal distribution. The log-normal model is commonly used in medicine and economics, where the basic process under consideration leads to a skewed distribution. One can often use a log-transformation to normalize the distribution of the original data. Even though the failure rate of the normal distribution is increasing, the failure rate of the log-normal distribution increases initially to a maximum and then decreases to zero as time approaches infinity. On the other hand, the mean residual life function (MRLF) exhibits a reverse behavior. It decreases initially and then increases. The authors of this paper deal with the monotonicity of the failure rate and the MRLF of a generalized log-normal distribution proposed by Chen (Ref. 1). This parametric family of distribution includes the log-normal distribution as a special case. The generalization is a three-parameter family which has the feature that one of the parameters can be regarded as playing the role of choosing a suitable transformation. Chen (Ref. 1) studied the parameter estimation and goodness-of-fit tests for fitting the generalized log-normal distribution to the electrical appliance data.
机译:众所周知,在许多实际应用中,数据遵循对数正态分布而不是正态分布。对数正态模型通常在医学和经济学中使用,其中所考虑的基本过程导致分布偏斜。人们通常可以使用对数转换来标准化原始数据的分布。即使正态分布的故障率不断增加,对数正态分布的故障率也先增加到最大值,然后随着时间趋于无穷大而减小到零。另一方面,平均剩余寿命函数(MRLF)表现出相反的行为。它先减少然后增加。本文的作者处理了由Chen(参考文献1)提出的广义对数正态分布的失效率和MRLF的单调性。此分布的参数族在特殊情况下包括对数正态分布。泛化是一个三参数族,其特征在于可以将其中一个参数视为选择合适变换的角色。 Chen(参考文献1)研究了参数估计和拟合优度测试,以将广义的对数正态分布拟合到电器数据中。

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