Some General Notions of Stochastic Orderings for Weighted Reliability and Uncertainty Measures with Applications

In this note, stochastic comparisons of reliability measures and related functions are presented. Inequalities for uncertainty of a residual life distribution and certain modified cross-entropy or discrimination information measures under weighted models are established. Comparisons of the expected uncertainty about the remaining lifetime of a component for weighted conditional distributions and unweighted conditional distributions are presented

Bounds and Comparisons for Weighted Renewal-Type Integral Equations

In this note, inequalities and bounds for weighted renewal-type integral equations are presented. Some upper and lower bounds for the weighted renewal-type integral equations with monotone weight functions are derived. Some upper and lower bounds for the weighted renewal-type equations with monotone weight functions are derived. Bounds for the difference between two weighted renewal functions as well between the parent and weighted renewal functions are obtained in terms of the parent renewal reliability functions and their first and second moments. Relations for renewal-type integrals of the ruin probability are presented. Some inequalities, bounds and convergence results are also established

On Inequalities and Partial Orderings for Weighted Reliability Measures

Inequalities, relations and partial ordering for weighted reliability measures are presented. Inequalities for Lévy distance measure for weighted distributions are obtained in terms of the parent distributions. Reliability inequalities and stability results are established for weighted distributions with monotone hazard and mean residual life functions

The Mc-Dagum Distribution and Its Statistical Properties with Applications

In this paper, a new class of distributions called Mc-Dagum distribution is proposed. This class of distributions contains several distributions such as beta-Dagum, beta-Burr III, beta-Fisk, Dagum, Burr III and Fisk distributions as special cases. The hazard function, reverse hazard function, moments, mean residual life function, Renyi entropy and Fisher information are obtained. Lorenz, Bonferroni and Zenga curves are derived. Maximum likelihood estimates of the model parameters and numerical examples are given to illustrate the usefulness of the proposed class of distributions

On Some Differential Equations

This paper investigates Cauchy and Goursat problems for partial differential operators. Successive approximation techniques for partial differential equations and the estimated results are employed to obtain the existence and the uniqueness of the solutions of such problems. An extended Darboux-Goursat-Beudon problem is studied

Generalizations of the Inverse Weibull and Related Distributions with Applications

In this paper, the generalized inverse Weibull distribution including the exponentiated or proportional reverse hazard and Kumaraswamy generalized inverse Weibull distributionsare presented. Properties of these distributions including the behavior of the hazard and reverse hazard functions, moments, coefficients of variation, skewness, andkurtosis, entropy, Fisher information matrix are studied. Estimates of the model parameters via method of maximum likelihood (ML), and method of moments (MOM) are presented for complete and censored data. Numerical examples are also presented

Theoretical Properties of the Weighted Feller-Pareto Distributions

In this paper, for the first time, a new six-parameter class of distributions called weighted Feller-Pareto (WFP) and related family of distributions is proposed. This new class of distributions contains several other Pareto-type distributions such as length-biased (LB) Pareto, weighted Pareto (WP I, II, III, and IV), and Pareto (P I, II, III, and IV) distributions as special cases. The pdf, cdf, hazard and reverse hazard functions, monotonicity properties, moments, entropy measures including Renyi, Shannon and s-entropies are derived

Establishment of Weak Conditions for Darboux-Goursat-Beudon Theorem

This paper is devoted to the establishment of weak conditions for Darboux-Goursat-Beudon (DGB) theorem in order to improve analogous results in [1, 7]. By adapting a technique proposed by [7] in another setting [8] via majorant method, we obtain the generalization of DGB theorem