M.Phil / MS
Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/63
This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.
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Item An extended Marshall-Olkin simulated Pareto-exponential distribution: development, properties and application(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Fazia Shahid; FA19-RST-002; Dr. Muhammad Mohsin; LHR TP 7204Marshal-Olkin simulated Pareto-exponential distribution (MOSPED) is a new distribution developed from simulated Pareto-Exponential distribution (SPED) by using Marshal-Olkin technique. SPED is a special distribution which emerges out as a marginal distribution of Bivariate Affine-Linear Exponential (BALE) distribution by Mohsin et al. (2014) without adopting any procedure. Some mathematical properties of the proposed distribution including moments, mean variance, incomplete moments are discussed along with its characterization. The reliability analysis of MOSPED comprising survival function, hazard function, reversed hazard function along with different types of entropies such as Renyi entropy, β-entropy and γ-entropy are presented. We also develop and discuss the distributions of series as well as parallel systems for the proposed distribution to observe the performance of each component in the product. Moreover, we estimate the unknown parameters of our model, parallel system and series system by using the method of maximum likelihood estimation for each distribution. A simulation study is performed to observe the stability and consistency of the model parameters. The application of the MOSPED is presented by using three real life data sets and its comparison with some baseline distributions is given on the basis of log-likelihood, AIC and BIC.Item Some Properties, Characterization and an Application of Mittag-Leffler type Poisson distribution(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) AYESHA ISRAR; SP19-RST-006; LHR TP 6537; Dr. Muhammad MohsinProbability distributions analyze the complex phenomena in a comprehensive way and provide the possible solutions of the understudy problem. The characteristics of a probability distribution describe its behavior and check its compatibility for modeling the data. The present research involves an extensive study of Mittag-Leffler type Poisson (MLTP) distribution developed by Porwal and Dixit (2017). They used Mittag-Leffler function, a mathematical function/series, to develop a new probability distribution. This function has been extensively used in the fields of mathematics, engineering, medical and social sciences. Some mathematical properties of the MLTP distribution are discussed. Graphical representation of MLTP distribution is provided for different values of the parameters. The moment generating function, characteristic function and order statistic are also studied. Characterizations for the sum of the random variables are presented. The distributions of product and ratio of two MLTP random variables are derived. In addition, the estimates of unknown parameters of MLTP distribution are obtained by using the method of maximum likelihood estimation. The MLTP distribution is applied to three real life data sets from the medical field. The log-likelihood values, AIC and BIC of the present model are compared with those of some other distributions extant in the literature.Item Bayesian Estimation of Inverse Rayleigh Distribution using Truncated Inverted Gamma as a Prior with different Loss Functions(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Sehrish Liaquat; FA17-RST-003; LHR TP 5744; Dr. Muhammad MohsinWe introduce the truncated prior in Bayesian analysis to refine the posterior distribution and get improved results. The parameter of Inverse Rayleigh (IR) distribution is estimated through Bayesian approach using various loss functions such as squared error loss function, entropy, general entropy, precautionary and squared log error loss function. Two types of Bayes estimators of the posterior expected risks for each loss function i.e. the truncated prior with the proper sampling distribution and the prior as a proper pdf with truncated sampling distribution are studied. In addition, the equal-tail credible intervals are constructed for all the cases. The simulation study is conducted to compare the different Bayes estimators along with the different procedures to seek the best estimators. A real life example is also presented to support the performance of the proposed technique.