$cdf of exponential distribution$

It has been getting great attention, since mixture models are more appropriate and multiple causes of failure can be simultaneously modeled. Mixture distributions have been used widely in reliability and survival analysis studies recently. Exponential and Weibull distributions are more popular than Gamma and log-Normal because the survival function of Gamma and log-Normal distributions doesn't have a closed form. Exponential, Gamma, Weibull and log-Normal distributions are some of the distributions commonly used for modeling lifetime data. Lifetime distributions have a significant role in Reliability theory and survival analysis. Keywords: Failure rate function, Reliability, Survival Analysis, Stress-Strength The maximum likelihood method is performed to estimate the parameters and a simulation study is conducted to validate the maximum likelihood estimators. We obtain the reliability of stress-strength model.

The basic mathematical properties including moments, generating functions, order statistics etc are derived. Thomas' College (Autonomous), Thrissur Kerala-680 001, India Email: this paper, mixture of Exponential and Weibull distributions is considered for modelling real lifetime data. On Exponential-Weibull Distribution Useful in Reliabilityĭepartment of Statistics, St.

Cdf of exponential distribution