逆Lomax分布的图像特征

Image Characteristics of Inverse Lomax Distribution

相比Lomax分布,逆Lomax分布可以模拟失效率为非单调形状的数据。针对逆Lomax分布,详细推导证明了其密度函数、失效率函数和平均失效率函数的形状特征,并给出了相应的图像。发现当0<α≤1时,其密度函数、失效率函数和平均失效率函数均为严格单调递减;而当α>0时,均为“倒浴盆”形。同时,也说明了逆Lomax分布的k阶矩不存在。

Compared with Lomax distribution,the inverse Lomax distribution can simulate the data with failure rate in a non-monotonic shape.For the inverse Lomax distribution,the shape characteristics of density function,failure rate function and average failure rate function are deduced in detail,and the corresponding images are given.It is found that the density function,failure rate function and average failure rate function are all strictly monotonically decreasing when 0<α≤1;while whenα>0,they are all in the shape of inverted bathtub.Besides,it also shows that the k-order moment of inverse Lomax distribution does not exist.