EP寿命分布的图像特征

Image Features of EP Lifetime Distribution

针对指数-泊松分布,首先,结合已知定理证明了该分布各阶矩E(xk)的存在性;其次,研究了分布的变异系数、偏度等数字特征与峰度λ参数的相关关系;最后,研究了分布失效率函数、平均失效率函数和平均剩余寿命函数等的图像特征,并证明了可靠性函数的单调性。得到了如下结论:指数-泊松分布的各阶矩存在;该分布的数字特征仅与参数λ有关,与参数β无关;失效率函数和平均失效率函数单调递减,平均剩余寿命函数单调递增。

For the Exponential-Poisson distribution,the existence of every moment E(xk)of the distribution is first proved by combining the known theorems.Secondly,the correlation between the numerical characteristics of coefficient of variation,skewness and kurtosis and the parameterλof the distribution is studied.Finally,the image features of failure rate function,average failure rate function and average remaining life function are studied,and the monotonicity of the reliability function is improved.The following conclusions are obtained:the Exponential-Poisson distribution’s moments exist;the numerical characteristics of the distribution are only related to the parameterλ,but have nothing to do with the parameterβ;the failure rate function and the average failure rate function decrease monotonically,and the average remaining life function increases monotonically.