Several New Extensions Of Life Distributions And Their Applications In Data Processing

For the past decades,distribution theory has focused on overcoming one of the challenging problems faced by the practitioners and applied statisticians in modeling random phenomena.The problem was addressed by proposing varieties of probability models and probability model generators that allow the use of the existing classical models to provide more flexible ones that can accommodate both monotonic and non-monotonic failure rates.In this thesis,we extended some classical and generalized models to a better and more flexible;we established several mathematical and statistical tools for better exploration of lifetime data in practice that arises in engineering,finance,stochastic modeling,reliability,etc.We have proposed five new probability models;among them,three are probability model generators.The proposed models are the Poisson-generalized half logistic distribution(Poi GHL);complementary Poisson-generalized half logistic distribution(CPGHL);exponentiated sineG generator of distribution(ESG);extended cosine-G generator of distributions(ECSG);and new extended beta-G generator of distributions(NEBG).The new models possess increasing,decreasing,unimodal,upside down bathtub,bathtub curve failure rates,and some other non-monotonic failure rates depending on the parameters.We derived and discussed the new models' mathematical and statistical properties,such as explicit expressions of the moments,Bonferroni and Lorenz curves,Shannon and Renyi entropy,stress-strength reliability parameter,quantile,log-transformation and characterization by truncated moments,the asymptotic of moments of residual life and extreme value distribution.Seven different estimation techniques are proposed to estimate the unknown parameters of the new models where possible.The estimation methods include maximum likelihood estimation(MLE),least-square estimation(LSE),weighted least-square estimation(WLSE),percentile estimation(PE),Anderson-Darling(AD),Cramer-von Mises(Cv M),and Bayes estimation(BE).We derived and investigated the stress-strength reliability parameter(R)of ESW and estimated by the maximum likelihood method.The maximum likelihood estimators of R turns-out to have a complicated information matrix which makes it difficult to obtain the confidence interval of R;we then employ the use of nonparametric percentile bootstrap(Bp)and student's bootstrap(Bt)confidence intervals and determine the approximate confidence interval of R.The stress-strength reliability studies from the ECSW is discussed and estimated using Bayes estimation by gamma prior under the square error loss function(SEL),absolute error loss function(AEL),maximum a posteriori(MAP),general entropy loss function(GEL),and the linear exponential loss function(LINEX).We developed a Monte Carlo simulation study to assess the performances of the estimators in each model by analyzing their bias and mean square error,and in practice,by real data set.The simulation results performance regarding each model was very good as the mean square error decreases when the sample sizes increases.Finally,at least in each model,two real data sets are used for illustration,in which our proposed models provided a better fit and outperformed some other popular distributions.The performance of the ESG and ECSG sub-models based on baseline Weibull distribution in stress-strength reliability presented that the models are a good candidate for reliability studies.In all the real data applications discussed that involved the model comparison,the goodness of fit and model selection measures considered are the Akaike information criterion(AIC),Bayesian information criterion(BIC),consistent Akaike information criterion(CAIC),Kolmogorov-Smirnov(KS),Anderson-Darling(AD),and Cram?er-von Mises(CvM).