Estimation of parameters of the Frechet -Frechet distribution using the transformed survival function with practical application
A thesis
Submitted to the council of the college of administration and Economic\ University of Karbala, as partial fulfillment of the requirements for the degree of Master of Science in statistic
By
Zahraa Hadi Abed Rahi
Under supervision
Mr. Dr. Mahdi Wahhab is the blessing of Nasrallah
The main idea of the thesis is a statistical study on a new probability distribution known as the Transmuted Survival Frechet Frechet Distribution ) ) (TSF.F) with three parameters (β,θ,λ), which was obtained by using a new formula, which is the transformed survival function formula Survival function Transmuted in which the survival function of the original Fregot distribution is used by adding a new parameter according to a special law of the mentioned formula
The new distribution (TSF.F) was obtained with three parameters (β, θ, λ), and then extracting the aggregate function (cdf) for the distribution and working on the derivation of the function to result in a probability function (pdf) for the new distribution (TSF.F) and after proving that the distribution is probabilistic, the Studying some important mathematical and statistical properties: the central visual moment around zero 〖E(X)〗^r and the decentralized moment about the mean 〖E(X-u)〗^r, as the arithmetic mean and variance obtained according to mathematical operations were found, as well as some other indicators Such as torsion, flattening, and coefficient of variation. Also, four methods were used to estimate the parameters of the proposed distribution, which are (the method of greatest possibility (ML), the method of ordinary least squares OLS, the method of weighted least squares (WLS), the method of linear quantitative moments LQ-moment
In the experimental aspect, Monte Carlo simulation was used to estimate the distribution parameters and reach the best method of estimation, as six models were used and default values for the distribution parameters were chosen with different sample sizes (small, medium and large) and using the statistical mean square error (MSE) criterion to obtain preference In estimation among the methods used, the OLS method was the best for estimating the parameters
. The new distribution was also applied to real data represented by renal failure, as the sample size is (91) people, representing the patient’s survival times until death, and the suitability of the distribution for the data was examined by using the good fit test (Kolmogorov-Smirnov test). The superiority of the (TSF.F) distribution in data representation compared to the Freget distribution before transformation. The survival function of the real data was also estimated using the best methods that were obtained in the experimental side (the usual least squares method). We found that the average patient survival rate is (0.51708), meaning that the patient’s survival rate is approximately 50%. A test was also conducted to choose the best probability distribution between the Freight distribution before conversion and the transformed distribution (TSF.F) according to three criteria, which are AIC standard, CAIC corrected standard, and BIC standard, and it was proved that the proposed transformed distribution is more appropriate and more flexible than the pre-transformation distribution
