On the Pareto Type III distribution
نویسنده
چکیده
This note analyzes the distributional properties of Pareto Type III random variables. The orignal two parameters distribution proposed by Pareto is expanded in a three parameters version and both its density and characteristic function are derived. The analytic expression of the inverse distribution function is also obtained, together with a simple series expansion of its moments of any order. Finally, we propose a simple statistical exercise designed to show the increased reliability of the Pareto Type III distribution in describing asymptotically dumped power-like behaviors.
منابع مشابه
Some Characterization Results on Generalized Pareto Distribution Based on Progressive Type-II Right Censoring
The progressive censoring scheme is a method of data collecting in reliability and life testing which has been of intensified interest in recent years. In the present paper, we prove some characterization results on generalized Pareto distribution based upon the independency and expected values of some functions of progressive type-II right censored order statistics.
متن کاملOptimal sample size and censoring scheme in progressively type II censoring based on Fisher information for the Pareto distribution
One of the most common censoring methods is the progressive type-II censoring. In this method of censoring, a total of $n$ units are placed on the test, and at the time of failure of each unit, some of the remaining units are randomly removed. This will continue to record $m$ failure times, where $m$ is a pre-determined value, and then the experiment ends. The problem of determining the optimal...
متن کاملShannon entropy in generalized order statistics from Pareto-type distributions
In this paper, we derive the exact analytical expressions for the Shannon entropy of generalized orderstatistics from Pareto-type and related distributions.
متن کاملCONSTANT STRESS ACCELERATED LIFE TESTING DESIGNWITH TYPE-II CENSORING SCHEME FOR PARETO DISTRIBUTION USING GEOMETRIC PROCESS
In many of the studies concerning Accelerated life testing (ALT), the log linear function between life and stress which is just a simple re-parameterization of the original parameter of the life distribution is used to obtain the estimates of original parameters but from the statistical point of view, it is preferable to work with the original parameters instead of developing inferences for the...
متن کاملInference about the Burr Type III Distribution under Type-II Hybrid Censored Data
This paper presents the statistical inference on the parameters of the Burr type III distribution, when the data are Type-II hybrid censored. The maximum likelihood estimators are developed for the unknown parameters using the EM algorithm method. We provided the observed Fisher information matrix using the missing information principle which is useful for constructing the asymptotic confidence...
متن کامل