Broderick O. Oluyede

A New Class of Generalized Lindley Distribution with Applications

A new four-parameter class of generalized Lindley (GL) distribution called the beta-generalized Lindley (BGL) distribution is proposed. This class of distributions contains the beta-Lindley, GL and Lindley distributions as special cases. Expansion of the density of the BGL distribution is obtained. The properties of these distributions, including hazard function, reverse hazard function, monotonicity property, shapes, moments, reliability, mean deviations, Bonferroni and Lorenz curves are derived. Measures of uncertainty such as Renyi entropy and s-entropy as well as Fisher information are presented. Method of maximum likelihood is used to estimate the parameters of the BGL and related distributions. Finally, real data examples are discussed to illustrate the applicability of this class of models.

Exponentiated Kumaraswamy-Dagum distribution with applications to income and lifetime data

A new family of distributions called exponentiated Kumaraswamy-Dagum (EKD) distribution is proposed and studied. This family includes several well known sub-models, such as Dagum (D), Burr III (BIII), Fisk or Log-logistic (F or LLog), and new sub-models, namely, Kumaraswamy-Dagum (KD), Kumaraswamy-Burr III (KBIII), Kumaraswamy-Fisk or Kumaraswamy-Log-logistic (KF or KLLog), exponentiated Kumaraswamy-Burr III (EKBIII), and exponentiated Kumaraswamy-Fisk or exponentiated Kumaraswamy-Log-logistic (EKF or EKLLog) distributions. Statistical properties including series representation of the probability density function, hazard and reverse hazard functions, moments, mean and median deviations, reliability, Bonferroni and Lorenz curves, as well as entropy measures for this class of distributions and the sub-models are presented. Maximum likelihood estimates of the model parameters are obtained. Simulation studies are conducted. Examples and applications as well as comparisons of the EKD and its sub-distributions with other distributions are given.Mathematics Subject Classification (2000)62E10; 62F30

Exponentiated power Lindley–Poisson distribution: Properties and applications

ABSTRACT A new four-parameter distribution called the exponentiated power Lindley–Poisson distribution which is an extension of the power Lindley and Lindley–Poisson distributions is introduced. Statistical properties of the distribution including the shapes of the density and hazard functions, moments, entropy measures, and distribution of order statistics are given. Maximum likelihood estimation technique is used to estimate the parameters. A simulation study is conducted to examine the bias, mean square error of the maximum likelihood estimators, and width of the confidence interval for each parameter. Finally, applications to real data sets are presented to illustrate the usefulness of the proposed distribution.

Exponential Dominance and Uncertainty for Weighted Residual Life Measures

In this article notions of exponential dominance and uncertainty for weighted and unweighted distributions are explored and used to compare values of the informational energy function and the differential entropy. Stochastic inequalities and bounds for cross-discrimination and uncertainty measures in weighted and unweighted residual life distribution functions and related reliability measures are presented. Momenttype inequalities for the comparisons of weighted and unweighted residual life distributions are also presented.

On Bounds And Approximating Weighted Distributions By Exponential Distributions

In this article, we obtain error bounds for exponential approximations to the classes of weighted residual and equilibrium lifetime distributions with monotone weight functions. These bounds are obtained for the class of distributions with increasing (decreasing) hazard rate and mean residual life functions.

Fixed and sequential designs for estimation in the exponential family with comparisons and applications to binomial proportions using beta priors

A sequential approach to the estimation of the difference of two population means for distributions belonging to the exponential family is adopted and compared with the best fixed design. Comparisons of sequential and best fixed designs for estimation of the difference between two Bernoulli proportions with beta priors are conducted. Results on the lower bound for the Bayes risk due to estimation and expected cost are presented and shown to be of first-order efficiency. Numerical comparisons for the Bernoulli distribution with beta priors are presented.

A new compound class of log-logistic Weibull–Poisson distribution: model, properties and applications

A new class of distributions called the log-logistic Weibull–Poisson distribution is introduced and its properties are explored. This new distribution represents a more flexible model for lifetime data. Some statistical properties of the proposed distribution including the expansion of the density function, quantile function, hazard and reverse hazard functions, moments, conditional moments, moment generating function, skewness and kurtosis are presented. Mean deviations, Bonferroni and Lorenz curves, Rényi entropy and distribution of the order statistics are derived. Maximum likelihood estimation technique is used to estimate the model parameters. A simulation study is conducted to examine the bias, mean square error of the maximum likelihood estimators and width of the confidence interval for each parameter and finally applications of the model to real data sets are presented to illustrate the usefulness of the proposed distribution.

Inequalities and comparisons of the cauchy, gauss, and logistic distributions

In this note, some inequalities and basic results including characterizations and comparisons of the Cauchy, logistic, and normal distributions are given. These results lead to necessary and sufficient conditions for the stochastic and dispersive ordering of the corresponding absolute random variables.

On stochastic inequalities and dependence orderings

Inequalities, local dependence orderings of reliability or survival functions of random variables are introduced and discussed. The notions of hazard dependence, stochastic orderings and exchangeability are studied and various important inequalities obtained. Examples and applications including inequalities and association for families of distribution functions satisfying the notions of stochastic and hazard dependence are presented.

Inequalities and bounds for kernel length-biased density estimation

In this note non-parametric estimates of the length-biased probability density function and related reliability measures are presented. Non-parametric estimates are also presented under random censoring. Inequalities and bounds for the error of kernel estimators used for the estimation of length-biased probability densities are obtained. Non-asymptotic bounds and stochastic convergence results are established. Inference for length-biased energy functions is developed and implemented.