Abstract
In this paper, a new four-parameter extended inverse Weibull distribution called Alpha power Extended Inverse Weibull Poisson distribution is introduced using the alpha power Poisson generator. This method adds two shape parameters to a baseline distribution thereby increasing its flexibility and applicability in modeling lifetime data. We study the structural properties of the new distribution such as the mean, variance, quantile function, median, ordinary and incomplete moments, reliability analysis, Lorenz and Bonferroni curves, Renyi entropy, mean waiting time, mean residual life, and order statistics. We use the method of maximum likelihood technique for estimating the model parameters of Alpha power extended inverse Weibull distribution and the corresponding confidence intervals are obtained. The simulation method is carried out to evaluate the performance of the maximum likelihood estimate in terms of their Absolute Bias and Mean Square Error using simulated data. Two lifetime data sets are presented to demonstrate the applicability of the new model and it is found that the new model has superior modeling power when compare to Inverse Weibull distribution, Alpha Power Poisson inverse exponential distribution, Alpha Power Extended Inverse Weibull distribution, and Alpha Power Extended Inverse Exponential distribution.
Highlights
IntroductionAdding an extra shape parameter to a classical (conventional) distribution is very common in statistical distribution theory
Adding an extra shape parameter to a classical distribution is very common in statistical distribution theory
We study the structural properties of the new distribution such as the mean, variance, quantile function, median, ordinary and incomplete moments, reliability analysis, Lorenz and Bonferroni curves, Renyi entropy, mean waiting time, mean residual life, and order statistics
Summary
Adding an extra shape parameter to a classical (conventional) distribution is very common in statistical distribution theory. Marshall and Olkin (1997) introduced another method that adds a parameter to any distribution function; two special cases were considered namely when X follows exponential or Weibull distribution and derived many properties of this proposed model. We study a new generalization called the Alpha power extended Inverse Weibull Poisson (APEIWP) distribution which possesses these properties. 2. The Model, Sub-Models, and Properties of Alpha Power Extended Inverse Weibull Poisson (APEIWP) Distribution. Suppose that X has at the Alpha power extended Inverse Weibull distribution where its PDF and CDF are given in (5) and (6) respectively. The Alpha power Extended Inverse Weibull Poisson distribution is the marginal CDF of X, given by 1 − exp −λ α. The graph shows that the hazard function of APEIWP model exhibits the non-monotone failure rate or upside-down bathtub failure rate for the values of the parameters considered
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Statistics and Probability
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
