https://gnedenko.net/Journal/2020/032020/RTA_3_2020.pdf
EXPONENTIAL-GAMMA (3,@) DISTRIBUTION AND ITS APPLICATIONS
Lifetime distributions for many components usually have a bathtub shape for its failure rate function in practice. However, there are a very few distribution have bathtub shaped failure rate function. Models with bathtub-shaped failure rate functions are useful in reliability analysis, particularly in reliability related decision making, cost analysis and burn-in analysis. When considering a failure mechanism, the failure of units in system may be due to random failure occurred by change in temperature, voltage, jurking etc or due to ageing. This paper study on a distribution, which is a mixture of Exponential and Gamma (3) distribution, which have bathtub shaped failure rate function. Moments, skewness, kurtosis, moment generating function, characteristic function are derived. Renyi entroy, Lorenz curve and Gini index are obtained. Reliability of stress-strength model is derived. Distribution of maximum and minimum order statistics are obtained. We have obtained maximum likelihood estimators. A simulation study is conducted to illustrate the performance of the accuracy of the estimation method used. Application is illustrated using real data.
