Abstract
In this work, the methods (Moments, Modified Moments, L-Moments, Percentile, Rank Set sampling and Maximum Likelihood) were used to estimate the reliability function and the two parameters of the Transmuted Pareto (TP) distribution. We use simulation to generate the required data from three cases this indicates sample size , and it replicates for the real value for parameters, for reliability times values we take .
 Results were compared by using mean square error (MSE), the result appears as follows :
 The best methods are Modified Moments, Maximum likelihood and L-Moments in first case, second case and third case respectively.
Highlights
Vilfredo Pareto [1] suggested the Pareto distribution, the and of the Pareto distribution, respectively. ( )Iraqi Journal of Science, 2022, Vol 63, No 2, pp: 652-666 Where, andShaw and Buckley [2] introduced the Quadratic Rank Transmutation Map (QRTM) that the relationship satisfies the cumulative distribution function approach. () ( ) () ( )| | ( ) ( )[ ( )]
Transmuted Pareto distribution (TP): Let X be a random variable of the (TP) distribution, both of the and for the (TP) distribution are expressed respectively as [8]
4. Experiments and Results: we review the simulation steps in terms of selecting sample sizes, real values of parameters and life time values that were used to estimate reliability: 1. The sample size is n=10, 30, 70, 100, and the sample which is replicated N=1000
Summary
Vilfredo Pareto [1] suggested the Pareto distribution, the (pdf) and (cdf) of the Pareto distribution, respectively. Shaw and Buckley [2] introduced the Quadratic Rank Transmutation Map (QRTM) that the relationship satisfies the cumulative distribution function (cdf) approach. Where ( ) is the (cdf), and ( ) is the (pdf) of the base distribution. Several authors used the quadratic rank transmutation map to find generalizations to some distributions. Some of them are Aryal and Tsokos [3] proposed the transmuted Weibull distribution. Aryal [4] proposed the transmuted log-logistic distribution. Proposed a transmuted new modified Weibull distribution. Elgarhy et al [7] proposed transmuted generalized quasi Lindley distribution. Faton and Llukan [8] proposed a transmuted Pareto distribution based on a Pareto distribution and a quadratic transmutation map. 2. Transmuted Pareto distribution (TP): Let X be a random variable of the (TP) distribution, both of the (pdf) and (cdf) for the (TP) distribution are expressed respectively as [8].
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