Journal of the Kerala Statistical Association

Some Problems Connected with the Distributions of Products and Ratios

Mathai A M — 2023-12-01

In this paper, the distributions of products and ratios involving real scalar positive variables, symmetric products and symmetric ratios of real positive definite matrices and symmetric product and symmetric ratios of Hermitian positive definite matrices in the complex domain are considered. Real scalar variable case is taken as a starting point. Here, it is pointed out how distributions of products and ratios are connected to Bessel integrals, reaction-rate probability integrals in nuclear reaction-rate theory, inverse Gaussian density, Kr¨atzel integral and transform, pathway transform, fractional integrals of the first and second kind etc. Only one
illustrative example each is given. Then, symmetric product and symmetric ratios of positive definite matrices in the real and complex domain are considered. Here also one illustrative example each is given. Some current research materials are also
mentioned in the introduction.

Generalized T – X Family of Distributions and Applications

K K Jose — 2023-12-01

In this paper, a new method of generating families of distributions using any p.d.f. as a generator which is called Transformed – Transformer ( T – X ) family of distributions is considered. Some members of this family including Gumbel – Uniform, Gumbel – Pareto, Gumbel – Frechet and their mathematical properties are explored. The method of maximum likelihood is used for estimating the distribution parameters. The flexibility of the new model is illustrated using real life data sets. Also industrial reliability test plans for acceptance or rejection of a lot of products submitted for inspection are developed. The acceptance sampling plan proposed here can save the test time in practical situations. Marshall – Olkin generalization of T – X family is also introduced. Stress-strength analysis is discussed. A simulation study is also conducted to study the behaviour of estimate of stress-strength reliability. Auto-regressive models are discussed based on Marshall – Olkin Gumbel uniform distribution and sample path properties are explored. Transmutation technique is also considered in T – X family. A real data is used to explain the flexibility of Gumbel Transmuted Uniform model, a member of Gumbel Transmuted X family.

A Mixture Regression Approach for Modelling Early Post Operative Hypocalcemia

Sreelaya K — 2023-12-01

In this paper, we show that a two component Laplace mixture model is an appropriate distribution to model postoperative calcium levels of patients undergoing thyroidectomy or surgery for thyroid diseases. A mixture regression model is constructed to predict postoperative calcium levels based on a pre-determined set of potential predictors. The parameters of the model are estimated using EM algorithm. Our study based on a real data set shows that two component Laplace mixture regression model is suitable for prediction and interpretation compared to the usual Gaussian mixture regression model.

A Versatile Probabilistic Model based on Yun-G Family of Distributions and its Applications in Engineering Sector

Akhila P — 2023-12-01

The present paper discusses a versatile three -parameter distribution from the Yun-G family. The important statistical properties like moments, stochastic ordering, and entropy are studied in this paper. Two characterizations of the distribution are obtained using the hazard rate function and truncated moments. The statistical inference of the distribution is studied by executing five different methods of parameter estimation, such as maximum likelihood estimation, ordinary least square method, weighted least square method, Cramer-von Mises method, and Anderson–Darling method. To study the fitting and applicability of the proposed distribution, two real life data sets from the engineering sector were analyzed and the proposed distribution is found to be more appropriate than the other competitive distributions. A comprehensive simulation study is also conducted and it showed the accuracy and consistency of the estimation techniques.

Bayesian Prediction of Future Order Statistics and k-Record Values based on Progressive Type-II Censored Sample for Generalized Exponential distribution

M Laji — 2023-12-01

In this paper, we consider the problem of two-sample Bayesian prediction of order statistics and lower k-record values from a future sample arising from a generalized exponential distribution based on progressively type-II censored sample. We obtain the Bayesian point predictors based on squared error and linex loss functions. It is observed that the predictors cannot be obtained in closed forms. So we propose importance sampling method to obtain the estimators for both point and interval predictors.