Building an InvertedTopp-Leone-Exponentinal Probability Distribution 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 written  by

Safa Najah Abdul-Ameer

Supervised By

Prof.Dr. Shrook A.S.AL-Sabbah

The process of fitting distributions is one of the common and well-known models for generating new distributions, which are the complex distributions. In this thesis, two methodologies were used for synthesis and to generate two new proposed distributions, and for the same single distributions, namely, the exponential distribution and (Inverted Topp-leone) using the two installation methodologies, which are the transformer method. (Transformed-Transformer Method (T-X family)) and the odd generalized exponential family (OGE)) and to generate the two distributions (Inverted Topp-leone-Exposnential) and symbolized by (I.T.L.E.D) and ( InvertedTopp_leone_ odd generalized Exponential Distribution) and symbolized by (I.T.L.OGE.D)) respectively with two parameters (θ and λ), where we symbolized the last distribution with the symbol (I.T.L.OGE.D) to distinguish it from the first distribution in the comparison process on the experimental side. In this thesis, a study of the properties of the two distributions (I.T.L.E.D) and (I.T.L.OGE.D) and the estimation of the reliability function in three ways, namely, the method of greatest possibility, the method of weighted least squares and the method of Kramer-Von, for the purpose of comparing the methods of estimation of the dependency function of the distribution In which he used the Monte Carlo simulation method and using the (Mathematica 12.2) program to implement the data programming to make a comparison between the two dependency functions and based on the statistical criteria which are the mean of error squares and using the Ranks method, where he used 5 different models for default values ​​of parameters and sample sizes The simulation results showed that the method of the greatest possibility (ML) in calculating the estimation of the reliability function of the two distributions (I.T.L.E.D) and (I.T.L.OGE.D) is the best method of estimation.Depending on the simulation results, by choosing the best method for estimating the reliability function of the two distributions (I.T.L.E.D) and (I.T.L.OGE.D) it is the method of greatest possibility (ML), especially for large volumes, as this method was adopted to represent the real data represented by the operating times of electrical transformers until failure, which amounted to The number of transfers was 95, during the period from January 2018 to 2021 in November.Among the Goodness of Fit Tests, it proved that the I.T.L.E.D distribution is the most suitable distribution for these types of data, because the P-Value values ​​were greater than the significance level α = 0.05. The reliability function of the distribution (I.T.L.E.D) was estimated.

Building an InvertedTopp-Leone-Exponentinal Probability Distribution 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 written  by

Safa Najah Abdul-Ameer

Supervised By

Prof.Dr. Shrook A.S.AL-Sabbah

The process of fitting distributions is one of the common and well-known models for generating new distributions, which are the complex distributions. In this thesis, two methodologies were used for synthesis and to generate two new proposed distributions, and for the same single distributions, namely, the exponential distribution and (Inverted Topp-leone) using the two installation methodologies, which are the transformer method. (Transformed-Transformer Method (T-X family)) and the odd generalized exponential family (OGE)) and to generate the two distributions (Inverted Topp-leone-Exposnential) and symbolized by (I.T.L.E.D) and ( InvertedTopp_leone_ odd generalized Exponential Distribution) and symbolized by (I.T.L.OGE.D)) respectively with two parameters (θ and λ), where we symbolized the last distribution with the symbol (I.T.L.OGE.D) to distinguish it from the first distribution in the comparison process on the experimental side. In this thesis, a study of the properties of the two distributions (I.T.L.E.D) and (I.T.L.OGE.D) and the estimation of the reliability function in three ways, namely, the method of greatest possibility, the method of weighted least squares and the method of Kramer-Von, for the purpose of comparing the methods of estimation of the dependency function of the distribution In which he used the Monte Carlo simulation method and using the (Mathematica 12.2) program to implement the data programming to make a comparison between the two dependency functions and based on the statistical criteria which are the mean of error squares and using the Ranks method, where he used 5 different models for default values ​​of parameters and sample sizes The simulation results showed that the method of the greatest possibility (ML) in calculating the estimation of the reliability function of the two distributions (I.T.L.E.D) and (I.T.L.OGE.D) is the best method of estimation.Depending on the simulation results, by choosing the best method for estimating the reliability function of the two distributions (I.T.L.E.D) and (I.T.L.OGE.D) it is the method of greatest possibility (ML), especially for large volumes, as this method was adopted to represent the real data represented by the operating times of electrical transformers until failure, which amounted to The number of transfers was 95, during the period from January 2018 to 2021 in November.Among the Goodness of Fit Tests, it proved that the I.T.L.E.D distribution is the most suitable distribution for these types of data, because the P-Value values ​​were greater than the significance level α = 0.05. The reliability function of the distribution (I.T.L.E.D) was estimated.