Interval Estimation  in inverse Weibull distribution of fuzzy data with

Practical Application

 A Thesis submitted to the Council of the College of Administration and Economics / University of Karbala

      as Partial fulfillment of the Requirements for   the Degree of Master of Science in Statistics

Presented by

Emtinan Sattar Eisaa

Supervised by

Ass .Prof .Dr .Mushtaq Kareem Abd Al -Rahem

The Inverse Weibull Distribution, which is a two-parameter one of the continuous probability distributions for life-time models, is one of the distributions in modeling death rates commonly used in Studying survival times, many data suffer from the problem of inaccuracy in their measurements and have different degrees of belonging to their groups. Therefore, we use data that addresses this problem and is called fuzzy data and is expressed in fuzzy numbers. Therefore, estimating the period in light of that data will lead to inaccuracy.  The accuracy of the estimates obtained when applying the traditional methods of estimation. Therefore, the concept of fuzziness must be generalized in our study to estimate the period in light of the fuzzy data. Therefore, three methods will be used to estimate the period for the parameters of the inverse Weibull distribution, namely, the method of greatest possibility, the method of White, and the method of relative greatest possibility in the case of life data.  For fuzzy numbers and the use of these estimates in estimating the fuzzy period of the distribution through a detailed simulation study using the Monte Carlo simulation method, where different values ​​of the distribution parameters were chosen and formed 6 different cases, as well as 5 different sample sizes (20,40,60,80,100) were compared.  The estimations of these methods are based on the statistical standard of mean square error (MSE) and the probability of coverage and according to the sizes of the samples. This work was carried out using  Through the MATIAB program, and finally, we used a model of local real data from the Holy Karbala Governorate for a sample (100) observations, which is the survival times for patients.  People with brain cancer through the application of the results learned from the experimental side .

Interval Estimation  in inverse Weibull distribution of fuzzy data with

Practical Application

 A Thesis submitted to the Council of the College of Administration and Economics / University of Karbala

      as Partial fulfillment of the Requirements for   the Degree of Master of Science in Statistics

Presented by

Emtinan Sattar Eisaa

Supervised by

Ass .Prof .Dr .Mushtaq Kareem Abd Al -Rahem

The Inverse Weibull Distribution, which is a two-parameter one of the continuous probability distributions for life-time models, is one of the distributions in modeling death rates commonly used in Studying survival times, many data suffer from the problem of inaccuracy in their measurements and have different degrees of belonging to their groups. Therefore, we use data that addresses this problem and is called fuzzy data and is expressed in fuzzy numbers. Therefore, estimating the period in light of that data will lead to inaccuracy.  The accuracy of the estimates obtained when applying the traditional methods of estimation. Therefore, the concept of fuzziness must be generalized in our study to estimate the period in light of the fuzzy data. Therefore, three methods will be used to estimate the period for the parameters of the inverse Weibull distribution, namely, the method of greatest possibility, the method of White, and the method of relative greatest possibility in the case of life data.  For fuzzy numbers and the use of these estimates in estimating the fuzzy period of the distribution through a detailed simulation study using the Monte Carlo simulation method, where different values ​​of the distribution parameters were chosen and formed 6 different cases, as well as 5 different sample sizes (20,40,60,80,100) were compared.  The estimations of these methods are based on the statistical standard of mean square error (MSE) and the probability of coverage and according to the sizes of the samples. This work was carried out using  Through the MATIAB program, and finally, we used a model of local real data from the Holy Karbala Governorate for a sample (100) observations, which is the survival times for patients.  People with brain cancer through the application of the results learned from the experimental side .