Weibull分布和指数分布以及均匀分布的关系研究

Study on the Relationship between Weibull Distribution and Exponential Distribution and Uniform Distribution

利用求随机变量函数分布的方法,证明了与Weibull分布相关的三条定理,通过定理的形式得出了Weibull变量和指数分布、均匀分布变量之间的转换关系,也得出了服从Rayleigh分布的随机变量和指数分布、均匀分布变量之间的转换关系,所得结论有利于通过指数分布和均匀分布来研究、分析Weibull分布。

By using the method of finding the distribution of random variable function,three theorems re- lated to Weibull distribution were proved,the transformation relation between Weibull variable and expo- nential distribution and uniform distribution was obtained by the form of theorem,the conversion relation between the random variable and the exponential distribution and the uniform distribution obeying Ray- leigh distribution was also obtained.The conclusion was helpful to study and analyze the Weibull distribu- tion by means of exponential distribution and uniform distribution.