The present paper is devoted to obtain the Bayes estimators of the unknown parameters of the Pareto Type II distribution under the assumptions of gamma priors on both the shape and scale parameters are considered. The Bayes estimators cannot be obtained in explicit forms. So we propose Markov Chain Monte Carlo (MCMC) techniques to generate samples from the posterior distributions and in turn computing the Bayes estimators. Point estimation and confidence intervals based on maximum likelihood is also proposed. The approximate Bayes estimators obtained under the assumptions of informative as well as non-informative priors, are compared with the maximum likelihood estimators using Monte Carlo simulations. One real data set has been analyzed for illustrative purposes.

Keywords: Pareto Type II Distribution, Record Values, Bayesian Estimation, Simulation and MCMC Techniques.

KEY WORDS: De-Noising, Wavelet, Daubechies and Filter

MSC 2020 Subject Classification: 62J05, 62P20, 65T60

Ideas of Knodel and Bohm-Hornik about walks in certain graphs, resembling the classical symmetric random walk on the integers, are combined. All the relevant generating functions (although occasionally quite involved) are made fully explicit. The treatment has an educational flavour as well.

Keywords: random walk, weighted edge, online bin-packing, generating functions, kernel method

A continuous probability model with three parameters named Modified Extended Kumaraswamy Exponential distribution is established using Extended Kumaraswamy Exponential distribution as base distribution through adding one more scale parameter.  Expressions for a number of functions, including the probability density function, skewness and kurtosis, survival function, hazard rate function, and distribution function, have been introduced in this context. Probability density curves and Hazard rate curves displayed. The hazard rate curves exhibit a monotonic increase, followed by a decrease, a period of constancy, constancy followed by an increase, and a J-shaped pattern across various parameter sets.  To assess the effectiveness of the developed model, we employed a real dataset on daily COVID-19 death counts in Nepal during the initial wave from January 23, 2020, to December 24, 2020. The model parameters were established using the techniques of least squares, maximum likelihood, and Cramer's-von Mises. To validate the model, we used Corrected Akaike's, Akaike's, Bayesian, and Hannan-Quinn Information Criteria. Furthermore, we utilized Q-Q and P-P plots for validation purposes. The goodness of fit can be assessed using Cramer-von Mises, Anderson-Darling tests and Kolmogorov-Smirnov tests. It's worth noting that all of these analyses and assessments are carried out within the R programming language environment, leveraging its powerful statistical and graphical capabilities. This ensures a systematic and thorough exploration of the model's validity and fitness for the given data.

Keywords: Corrected Akaike’s Information; COVID-19; Goodness of fit; Hazard rate function; New Kw-G family.

We introduce a new family of equivalence tests for a fully specied continuous distribution on R. The tests are based on the weighted L2- distance between cumulative distribution functions. The asymptotic dis- tribution of the test statistic is derived using the functional delta method. The local asymptotic optimality of the proposed tests is shown. An easy- to-compute estimator for the asymptotic variance of the test statistic is provided. The tests can be carried out using the asymptotic approxima- tion or the percentile-t bootstrap method. For the special case of the Anderson-Darling distance, a comprehensive simulation study of nite sample properties is performed. A practical method of nding appropri- ate values for the tolerance parameter is given.

MSC 2020: 62G10
Key words: equivalence test, Cramér-von Mises distance, Anderson-Darling distance, uniformity test, weighted CDF