On The Weighted BurrXII Distribution: Theory and Practice

We take an in-depth look at the weighted Burr-XII distribution. This distribu-tion generalizes Burr-XII, Lomax, and log-logistic distributions. We discuss the dis-tributional characteristics of the probability density function, the failure rate function,and mean residual lifetime of this distribution. Moreover, we obtain various statisti-cal properties of this distribution such as moment generating function, entropies, meandeviations, order statistics and stochastic ordering. The estimation of the distributionparameters via maximum likelihood method and the observed Fisher information ma-trix are discussed. We further employ a simulation study to investigate the behavior ofthe maximum likelihood estimates (MLEs). A test concerning the existence of size-biasin the sample is provided. In the end, a real data is presented and is analyzed usingthis distribution along with some existing distributions for illustrative purposes

Estimating the Parameters of Rayleigh Cumulative Exposure Model in Simple Step-Stress Testing. Natasha Beretvas is an

Assumes the life distribution of a test unit for any stress follows a Rayleigh distribution with scale parameterθ , and that Ln(θ ) is a linear function of the stress level. Maximum likelihood estimators of the parameters under a cumulative exposure model are obtained. The approximate variance estimates obtained from the asymptotic normal distribution of the maximum likelihood estimators are used to construct confidence intervals for the model parameters. A simulation study was conducted to study the performance of the estimators. Simulation results showed that in terms of bias, mean squared error, attainment of the nominal confidence level, symmetry of lower and upper error rates and the expected interval width, the estimators are very accurate and have a high level of precision

On Combining Independent Tests In Case Of Log-Logistic Distribution

Bahadur's stochastic comparison of asymptotic relative efficiency of combining infinitely independent tests in case of log-logistic distribution is proposed. Six free-distribution combination producers namely; Fisher, logistic, sum of p-values, inverse normal, Tippett's method and maximum of p-values were studied. Several comparisons among the six procedures using the exact Bahadur's slopes were obtained. These non-parametric procedures depend on the p-value of the individual tests combined

Optimum Times for Step-Stress Cumulative Exposure Model Using Log-Logistic Distribution with Known Scale Parameter

Abstract: In this paper we assume that the life time of a test unit follows a log-logistic distribution with known scale parameter. Tables of optimum times of changing stress level for simple step-stress plans under a cumulative exposure model are obtained by minimizing the asymptotic variance of the maximum likelihood estimator of the model parameters at the design stress with respect to the change time. Zusammenfassung: In diesem Aufsatz wird angenommen, dass die Lebensdauer einer Testeinheit einer log-logistischen Verteilung mit bekanntem Skalenparameter genügt. Tabellen für die optimalen Zeitpunkte eines Wechsels des Belastungsniveaus für einfache step-stress Pläne unter einem kumulativen Expositionsmodells erhält man durch Minimieren der asymptotischen Varianz des Maximum Likelihood Schätzers der Modellparameter zur zulässigen Spannung bezüglich der Wechselzeit

Combining Independent Tests of Conditional Shifted Exponential Distribution

The problem of combining n independent tests as n→∞ for testing that variables are uniformly distributed over the interval (0, 1) compared to their having a conditional shifted exponential distribution with probability density function f (xθ ) = e−(x−γθ) , x ≥γθ , θ ∈[a,∞), a ≥ 0 was studied. This was examined for the case where θ1, θ2, … are distributed according to the distribution function (DF) F and when the DF is Gamma (1, 2). Six omnibus methods were compared via the Bahadur efficiency. It is shown that, as γ → 0 and γ → ∞ , the inverse normal method is the best among the methods studied

Acceptance Sampling Plans Based on Truncated Life Tests in the Inverse-Gamma Model

In this article, acceptance sampling plans are suggested for the life test that is truncated at a preassigned time. The life time of the test units are assumed to follow the inverse-gamma distribution. The minimum sample sizes necessary to ensure the specified mean life is obtained. The operating characteristic function values of the proposed sampling plans and the producer's risk are provieded. Some tables are given and the results are illustrated by numerical examples