Estimating the reliability of an extended power function distribution using (NLTE-X Family) with practical application

A Thesis Submitted to

Council of  The Administration and Economics/ Karbala

University as Partial fulfillment of the Requirements for

the Degree of Master of Science in Statistics

Presented by

Falah Hassan Jabbar Abdul-Hassan

Under supervision

Ass .Prof .Dr. Enas Abdu Alhafudh Mohammed

The process of expanding probability distributions is one of the important processes that has grown in importance exponentially over the past few decades, this is due to the increased ability of classical distributions to represent real data on a larger scale and accuracy, the process of extending distributions using families and derived classes is one of the methods recently used to extend distributions, In this letter, The new lifetime exponential- X family is used (NLTE-X Family) in constructing a new probabilistic model called (The new lifetime exponential- Power function distribution) ” NLTE-PF” The proposed model is an extension of the power function distribution, Some of its statistical properties were studied, the coefficients and reliability function of the new probabilistic model were estimated by four estimation methods,( Maximum Likelihood Estimators, Least square Method, Method of Percentiles Estimators, Maximum product of spacing estimation method), A brief simulation study was carried out using the method (Monte Carlo) to evaluate the performance of parameter estimates and reliability function estimates for the new model using the four methods, This work was performed by Mathematica 12.2 software packages, Several experiments were conducted with small, medium and large sample sizes 4 different sample sizes (25,50,75,100), The statistical standard was used, the mean of squares of error to compare the four estimation methods for parameter estimations, Mean integral error squares  to compare the four estimation methods for the reliability function estimator.

The new probabilistic model (NLTE-PF) was applied to real data with (96) observations representing continuous positive airway pressure device operating times until failure. The comparison was made between the (NLTE-PF) distribution and the power function (PF) distribution, the new model gave greater flexibility and efficiency in representing real data and proved to be superior to the power function (PF) distribution. The reliability function for the Maximum Likelihood Estimators (NLTE-PF) distribution was estimated, which outperformed other methods for estimating the reliability function for medium and large sample sizes

Estimating the reliability of an extended power function distribution using (NLTE-X Family) with practical application

A Thesis Submitted to

Council of  The Administration and Economics/ Karbala

University as Partial fulfillment of the Requirements for

the Degree of Master of Science in Statistics

Presented by

Falah Hassan Jabbar Abdul-Hassan

Under supervision

Ass .Prof .Dr. Enas Abdu Alhafudh Mohammed

The process of expanding probability distributions is one of the important processes that has grown in importance exponentially over the past few decades, this is due to the increased ability of classical distributions to represent real data on a larger scale and accuracy, the process of extending distributions using families and derived classes is one of the methods recently used to extend distributions, In this letter, The new lifetime exponential- X family is used (NLTE-X Family) in constructing a new probabilistic model called (The new lifetime exponential- Power function distribution) ” NLTE-PF” The proposed model is an extension of the power function distribution, Some of its statistical properties were studied, the coefficients and reliability function of the new probabilistic model were estimated by four estimation methods,( Maximum Likelihood Estimators, Least square Method, Method of Percentiles Estimators, Maximum product of spacing estimation method), A brief simulation study was carried out using the method (Monte Carlo) to evaluate the performance of parameter estimates and reliability function estimates for the new model using the four methods, This work was performed by Mathematica 12.2 software packages, Several experiments were conducted with small, medium and large sample sizes 4 different sample sizes (25,50,75,100), The statistical standard was used, the mean of squares of error to compare the four estimation methods for parameter estimations, Mean integral error squares  to compare the four estimation methods for the reliability function estimator.

The new probabilistic model (NLTE-PF) was applied to real data with (96) observations representing continuous positive airway pressure device operating times until failure. The comparison was made between the (NLTE-PF) distribution and the power function (PF) distribution, the new model gave greater flexibility and efficiency in representing real data and proved to be superior to the power function (PF) distribution. The reliability function for the Maximum Likelihood Estimators (NLTE-PF) distribution was estimated, which outperformed other methods for estimating the reliability function for medium and large sample sizes