K. K. Jose

Applications of Marshall–Olkin Fréchet Distribution

In this article, we consider the applications of Marshall–Olkin Fréchet distribution. The reliability of a system when both stress and strength follows the new distribution is discussed and related characteristics are computed for simulated data. The model is applied to a real data set on failure times of air-conditioning systems in jet planes and reliability is estimated. We also develop acceptance sampling plan for the acceptance of a lot whose lifetime follows this distribution. Four different autoregressive time series models of order 1 are developed with minification structure as well as max-min structure having these stationary marginal distributions. Some properties of the models are also established.

Generalized Mittag-Leffler Distributions and Processes for Applications in Astrophysics and Time Series Modeling

Geometric generalized Mittag-Leffler distributions having the Laplace transform \(\frac{1} {1+\beta \log (1+{t}^{\alpha })},0 0\) is introduced and its properties are discussed. Autoregressive processes with Mittag-Leffler and geometric generalized Mittag-Leffler marginal distributions are developed. Haubold and Mathai (Astrophysics and Space Science 273 53–63, 2000) derived a closed form representation of the fractional kinetic equation and thermonuclear function in terms of Mittag-Leffler function. Saxena et al. (2002; Astrophysics and Space Science 209 299–310 2004a; Physica A 344 657–664 2004b) extended the result and derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions. These results are useful in explaining various fundamental laws of physics. Here we develop first-order autoregressive time series models and the properties are explored. The results have applications in various areas like astrophysics, space sciences, meteorology, financial modeling and reliability modeling.

An autoregressive process with geometric α-laplace marginals

Geometric Laplace and geometric α-Laplace distributions are studied and certain limit properties are derived. An autoregressive process with geometric Laplace stationary marginal distribution is introduced and its properties are studied. These results are generalized to geometric α-Laplace case also and applications are discussed.

On the q-Weibull Distribution and Its Applications

The q-Weibull distribution is a stretched model for Weibull distribution, obtained by introducing a new pathway parameter q, which facilitates a slow transition to the Weibull as q → 1. In this article, we make a detailed study of the properties of the q-Weibull distribution and we apply it to a data on cancer remission times for which this distribution is a better fit than Weibull. Results relating to reliability properties, estimation of parameters, and applications in stress-strength analysis are also obtained.

Comparing Two Process Capability Indices under Balanced One-Way Random Effect Model

Process capability indices such as Cp, Cpk, Cpmk and Cpm are widely used in manufacturing industries to provide a quantitative measurement of the performance of the products. In this article, we derived generalized confidence intervals for the difference between process capability indices for two processes under one-way random effect model. Our study provides coverage probability close to the nominal value in almost all cases as shown via simulation. An example from industrial contexts is given to illustrate the results. Copyright

A Subordinated Process with Geometric Exponential Operational Time

In this note a subordinated process with Geometric Exponential operational time is introduced and studied.

On Confidence Intervals for Process Capability Indices in a One-Way Random Model

In this article, we investigated the bootstrap calibrated generalized confidence limits for process capability indices C pk for the one-way random effect model. Also, we derived Bissells approximation formula for the lower confidence limit using Satterthwaites method and calculated its coverage probabilities and expected values. Then we compared it with standard bootstrap (SB) method and generalized confidence interval method. The simulation results indicate that the confidence limit obtained offers satisfactory coverage probabilities. The proposed method is illustrated with the help of simulation studies and data sets.

Generalized Laplacian Distributions and Autoregressive Processes

Generalized Laplacian distribution is considered. A new distribution called geometric generalized Laplacian distribution is introduced and its properties are studied. First- and higher-order autoregressive processes with these stationary marginal distributions are developed and studied. Simulation studies are conducted and trajectories of the process are obtained for selected values of the parameters. Various areas of application of these models are discussed.

Confidence Intervals for Process Capability Indices for the Unbalanced One‐Way Random Effect ANOVA Model

Confidence intervals for process capability index Cpk are developed for the unbalanced one-way random effect model using Bissells approximation method. The proposed limit is compared with the generalized lower confidence limit obtained using the generalized pivotal quantity method. To assess the accuracy of the method, a simulation study is presented. The results are illustrated with an industrial example. Copyright

On Record Values and Reliability Properties of Marshall–Olkin Extended Exponential Distribution

The Marshall–Olkin Extended Exponential distribution is introduced and reliability properties are studied. The p.d.f.’s of nth record value, joint p.d.f.’s, of mth and nth record values are derived to obtain the expression for mean, variance and covariance of reord values. The entropy of jth record value is derived.The stress strength analysis for the new model is carried out. We develop autoregressive processes and sample path properties are explored. The results are verified using simulations as well as graphical studies.The model is extended to higher orders also.