Abstract
In this study, a new method is proposed for generating families of the sum of the hazard functions for two distributions named the Σh distributions. This new family will help in the application of a wider range of life time data. Many new distributions, which are members of the family, are presented with emphasis on the Σh Exponential-Lomax distribution. Details and various statistical properties have been introduced. The maximum likelihood estimation for parameters of the Σh Exponential-Lomax distribution has also been discussed alongside Monte Carlo simulation study to assess the accuracy and the performance of the estimation procedure. Finally, the Σh Exponential-Lomax distribution has been fitted to a real data set to provide variability of its applicability.
Highlights
Probability distributions have been popularly used in many areas of the real world situations
Which creates a clear need for the extended version of these classical distributions? Serious attempts have been made in this regard to propose new families of distributions that extend the existing well-known distributions
We presented a new family of distributions called the Σh distributions
Summary
Probability distributions have been popularly used in many areas of the real world situations. Gupta et al (1998) proposed to model failure time data by F*(f) = [F(t)]θ where F(t) is the baseline distribution function and θ is a positive real number. We developed the hazard function “h” of the distributions to find that we can have the sum of the hazard functions of two distributions by adding the hazard function of the first distribution to the hazard function of the second distribution This is to improve the characteristics and flexibility of the existing distributions and to introduce the extended version of the baseline distribution having closed form of the hazard function. This proposed family set out on the formation of new distributions by incorporating n distributions together.
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