In this study, the statistical inference problem for geometric process (GP) is considered when distribution of first occurrence time assumed to be inverse Gaussian (IG). The parameters a, μ and σ2 GP are estimated by using maximum likelihood (ML) method, where ratio GP, mean variance IG distribution, respectively. Asymptotic distributions consistency properties ML estimators obtained. These asymptotic enable us give a test statistic which distinguishes renewal from process. Monte Carlo...

Geometric process (GP) is widely used as a non-stationary stochastic model in reliability analysis. In many of applications related with GP its mean value and variance functions are needed. Since there no analytical forms these lot situations their computations importance. this study, numerical approximation Monte Carlo estimation method based on the convolutions distribution have been proposed for both functions.

The aim of this study is to investigate the solution statistical inference problem for geometric process (GP) when distribution first occurrence time assumed be Rayleigh. Maximum likelihood (ML) estimators parameters GP, where a and λ are ratio parameter GP scale Rayleigh distribution, respectively, obtained. In addition, we derive some important asymptotic properties these such as normality consistency. Then run simulation studies by different values compare estimation performances obtained...

Abstract The geometric process is considered when the distribution of first interarrival time assumed to be Weibull. Its one‐dimensional probability derived as a power series expansion convolution Weibull distributions. Further, mean value function expanded into using an integral equation. © 2014 Wiley Periodicals, Inc. Naval Research Logistics, 61: 599–603,

Abstract In this article, an integral equation satisfied by the second moment function M 2 ( t ) of a geometric process is obtained. The numerical method based on trapezoidal integration rule proposed Tang and Lam for adapted to solve equation. To illustrate method, first interarrival time assumed be one four common lifetime distributions, namely, exponential, gamma, Weibull, lognormal. addition power series expansion derived using ), when has exponential distribution.

Gamma, lognormal and Weibull distributions are most commonly used in modeling asymmetric data coming from the areas of life testing reliability engineering. In this study, we deal with problem selecting one these for a given set which is consistent geometric process (GP) model according to T-statistic based on ratio maximized likelihood (RML). First, show that performs better than Kolmogorov- Smirnov (KS), mean square error (MSE) maximum percentage (MPE) extensive simulation study. Then, by...

Statistical inferences for the geometric process (GP) are derived when distribution of first occurrence time is assumed to be inverse Gaussian (IG). An α-series process, as a possible alternative GP, introduced since GP sometimes inappropriate apply some reliability and scheduling problems. In this study, statistical inference problem considered where IG. The estimators parameters α, μ, σ2 obtained by using maximum likelihood (ML) method. Asymptotic distributions consistency properties ML...

The explicit estimators of the parameters α, μ and σ2 are obtained by using methodology known as modified maximum likelihood (MML) when distribution first occurrence time an event is assumed to be Weibull in series process. efficiencies MML compared with corresponding nonparametric (NP) it shown that proposed have higher than NP estimators. In this study, we extend these results case, where Gamma. It another widely used well-known reliability analysis. A real data set taken from literature...

The α-series process (ASP) is widely used as a monotonic stochastic model in the reliability context. So parameter estimation problem an ASP of importance. In this study for considered when distribution first occurrence time event assumed to be lognormal. parameters α, μ and σ2 are estimated via maximum likelihood (ML) method. Asymptotic distributions consistency properties these estimators derived. A test statistic conducted distinguish from renewal (RP). Further, modified moment (MM)...

The geometric process (GP) has been widely utilized as a stochastic monotone model in the fields of probability and statistics. However, its practical application is often limited by certain assumptions. To address this, [Wu (2018). Doubly applications. Journal Operational Research Society, 69(1), 66–67] introduced doubly (DGP) an extension GP model, relaxing some Due to ability overcome limitations DGP gained significant popularity recent times. This study focuses on parameter estimation...

The α-series process is an important counting commonly used to model data sets having monotonic trend. It especially utilized in reliability analysis of deteriorating systems and warranty repairable systems. When a set compatible with the process, it make inference for parameters process. All studies literature only consider single realization which has complete samples. However, multi-sample may be observed. In this situation, includes both censored study, estimation problem under studied...

ABSTRACT This article is concerned with some parametric and nonparametric estimators for the k-fold convolution of a distribution function. An alternative estimator proposed its unbiasedness, asymptotic consistency properties are investigated. The normality this established. Some applications given in renewal processes. Finally, computational procedures described relative performance these small sample sizes investigated by simulation study. Keywords: ConvolutionEmpirical dfRenewal processes...

The main objective of this paper is to determine the best estimators shape and scale parameters two parameter Weibull distribution. Therefore, both classical Bayesian approximation methods are considered. For estimation maximum likelihood (MLEs), modified estimators-I (MMLEs-I), -II (MMLEs-II), least square (LSEs), weighted (WLSEs), percentile (PEs), moment (MEs), L-moment (LMEs) TL- (TLMEs) used. Since don't have explicit form. There Bayes obtained by using Lindley's Tierney Kadane's in...

There is no doubt that finding the estimators of model parameters accurately and efficiently very important in many fields. In this study, we obtain explicit unknown gamma geometric process (GP) via modified maximum likelihood (MML) methodology. These are as efficient (ML) estimators. The marginal joint asymptotic distributions MML also derived efficiency comparisons between ML made through an extensive Monte Carlo simulations. Moreover, a real data example considered to illustrate...

In this paper, we deal with the problem of estimating delayed renewal and variance functions in processes. Two parametric plug-in estimators for these are proposed their unbiasedness, asymptotic unbiasedness consistency properties investigated. The normality established. Further, a method computation is given. Finally, performances evaluated small sample sizes by simulation study.