Convolution of generated random variable from exponential distribution with stabilizer constant

Abstract

The new distribution is constructed by generating random variables from an exponential distribution with stabilizer constant. It is presented the convolution from this identically and independent new random variable by using analytical methods in the form of probability density function and cumulative distribution function. In addition, it is presented some properties of the exponential distribution with stabilizer constant and its convolution including mean, variance, moment generating function, characteristic function, skewness and kurtosis.

The Use Of MEWMA Control Chart In Controlling Major Component Of Cement Product

“…N et al [5] explain that EWMA control chart for monitoring exponential distributed quality characteristics where the exponential distribution contained the characteristic function and term of convolution had researched by Devianto [6] and [7]. The sum of exponential distribution is the hypoexponential distribution can setting by stabilizer constant such as describe by Devianto et al [8] and [9]. TheMEWMA control chart is used to simultaneously monitor several correlated process variables [10].…”

The Property of Continuity And Positively Definite Characteristic Function of Compound Poisson Distribution As The Sum of Geometric Distribution

“…In addition, this sum of independent random variables can be de ned as convolution of a distribution. Some theories of convolution have been developed by previous researcher on some articles, Devianto et al (2015) have introduced convolution of generated random variable from exponential distribution with stabilizer constan. Another reasearch related to convolution is explained by Serfozo (1986) where the paper introduced compound Poisson approximation for sums of random variables.…”

The uniform continuity of characteristic function from convoluted exponential distribution with stabilizer constant

“…Devianto et al [3] have introduced convolution of generating random variables from exponential distribution with stabilizer constant. It is worth to give some properties of characteristic function from this new distribution.…”

“…Devianto et al [3] has shown the convolution of this new intoduced distribution by setting W1, W2, ..., Wn be n independent and identically exponential distribution with stabilizer constant where probability density function is defined as follows …”