Shanker、Akash、Ishita、Pranav、Rani和Ram Awadh分布的独立随机变量和
Sum of independent random variable for Shanker, Akash, Ishita, Pranav, Rani and Ram Awadh distributions
摘要：
在统计学和概率论中，最重要的统计量之一是随机变量的和。在引入一个概率分布之后，确定n个独立同分布随机变量之和是作者感兴趣的话题之一。本文给出了Shanker、Akash、Ishita、Rani、Pranav和Ram Awadh等n个独立同分布随机变量之和的密度函数。为了确定所有上述分布，应用基于变量变化技术的问题求解方法。它们的m阶矩也被精确计算。此外，在Lindley部件失效时间下，还对n取1冷备系统的可靠性和平均失效时间进行了评估。
英文摘要：
In statistics and probability theory, one the most important statistics is the sums of random variables. After introducing a probability distribution, determining the sum of n independent and identically distributed random variables is one of the interesting topics for authors. This paper presented the probability density function for the sum of n independent and identically distributed random variables such as Shanker, Akash, Ishita, Rani, Pranav and Ram Awadh. In order to determine all aforementioned distributions, the problem-solving methods are applied which is based on the change-of-variables technique. The mth moments for them were also accurately calculated. Besides, the reliability and the mean time to failure of a 1 out of n cold standby spare system has also been evaluated under the Lindley components failure time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
