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 hypoexponential distribution is the distribution of the sum of independent exponential random variables with different parameters, this sum is also known as convolution. This paper is introduced new probability density function by setting stabilizer constant to hypoexponential distribution, this stabilizer constant is used to maintain the nature of probability density function. Some properties of this new distribution are presented in third and fourth moments, skewness, kurtosis and their relations.Mathematics Subject Classification: 97K50, 60E05, 44A35.