Weibull-Pareto Distribution Research Articles

A Note on Class of Weibull–Pareto Distribution

A Note on Class of Weibull–Pareto Distribution

Designing of Single Acceptance Sampling Plan based on Time Truncated Life Test under New Weibull-Pareto Distribution

Designing of Single Acceptance Sampling Plan based on Time Truncated Life Test under New Weibull-Pareto Distribution

Optimal and economic design of modified double sampling plan under new Weibull–Pareto distribution

PurposeThe purpose of this paper is to design a modified version of the double sampling plan to handle the inspection processes requiring a minimum sample size to assure the median life for the products under the new Weibull–Pareto distribution. The economic design of the proposed plan is also considered to assure the product's lifetime with minimum cost.Design/methodology/approachThe authors have developed an optimization model for obtaining the required plan parameters by solving simultaneously two non-linear inequalities and such inequalities have been formed based on the two points on the operating characteristic curve approach.FindingsThe results show that the average sample number, average total inspection and total inspection cost under the proposed plan are smaller than the same of a single sampling plan. This means that the proposed plan will be more efficient than a single sampling plan in reducing inspection effort and cost while providing the desired protection.Originality/valueThe proposed modified double sampling plan designed to assure the median life of the products under the new Weibull–Pareto distribution is not available in the literature. The proposed plan will be very useful in assuring the product median lifetime with minimum sample size as well as minimum cost in all the manufacturing industries.

General Entropy with Bayes Techniques under Lindley and MCMC for Estimating the New Weibull–Pareto Parameters: Theory and Application

Censored data play a pivotal role in life testing experiments since they significantly reduce cost and testing time. Hence, this paper investigates the problem of statistical inference for a system of progressive first-failure censoring data for a new Weibull–Pareto distribution. Maximum likelihood estimates for the parameters as well as some lifetime indices such as reliability, hazard rate functions, and coefficient of variation are derived. Lindley approximation and the Markov chain Monte Carlo technique are applied to obtain the Bayes estimates relative to two different loss functions: balanced linear exponential and general entropy loss functions. The results of the Bayes estimate are computed under the consideration of informative prior function. A real-life example "the survival times in years of a group of patients given chemotherapy treatment" is presented to illustrate the proposed methods. Finally, a simulation study is carried out to determine the performance of the maximum likelihood and Bayes estimates and compare the performance of different corresponding confidence intervals.

Alpha Power Exponentiated New Weibull-Pareto Distribution: Its Properties and Applications

In this paper, a new five-parameter model called alpha power exponentiated new Weibull-Pareto distribution is introduced based on a new developing technique. We derived some properties relating to the proposed distribution, including moments, moment generating function, quantile function, mean residual life and mean waiting time, and order statistics of the new model. The model parameters are estimated using the maximum likelihood method. Some simulation studies are performed to investigate the effectiveness of the estimates. Finally, we used three real-life data sets to show the flexibility of the introduced distribution.

Extended Odd Weibull Pareto Distribution, Estimation and Applications

Extended Odd Weibull Pareto Distribution, Estimation and Applications

Stress – strength p(X

In this paper, is derived the reliability of an n-cascade stress-strength system based on the New Weibull-Pareto Distribution (NWPD) with known β and θ parameters, λ unknown λ parameter, for probability of n- components having X, Z two stresses between them strengths Y. In NWPD, there are four methods of parameters and this system reliability estimators (the Maximum Likelihood, Moments, Least Square and Weighted Least Square Methods) are discussed, based estimators on the simulation technique, these estimates are compared by criteria the mean square error were used to compare small, medium and large samples. It has been concluded that the greatest maximum likelihood estimator performs all of the other options considered.

One- and Two-Sample Predictions Based on Progressively Type-II Censored Carbon Fibres Data Utilizing a Probability Model.

New Weibull-Pareto distribution is a significant and practical continuous lifetime distribution, which plays an important role in reliability engineering and analysis of some physical properties of chemical compounds such as polymers and carbon fibres. In this paper, we construct the predictive interval of unobserved units in the same sample (one sample prediction) and the future sample based on the current sample (two-sample prediction). The used samples are generated from new Weibull-Pareto distribution due to a progressive type-II censoring scheme. Bayesian and maximum likelihood approaches are implemented to the prediction problems. In the Bayesian approach, it is not easy to simplify the predictive posterior density function in a closed form, so we use the generated Markov chain Monte Carlo samples from the Metropolis-Hastings technique with Gibbs sampling. Moreover, the predictive interval of future upper-order statistics is reported. Finally, to demonstrate the proposed methodology, both simulated data and real-life data of carbon fibres examples are considered to show the applicabilities of the proposed methods.

New Probability Distributions in Astrophysics: VIII. The Truncated Weibull—Pareto Distribution

New Probability Distributions in Astrophysics: VIII. The Truncated Weibull—Pareto Distribution

Acceptance Sampling Plans from Life Tests Based on Percentiles of New Weibull–Pareto Distribution with Application to Breaking Stress of Carbon Fibers Data

In this paper, acceptance sampling plans (ASPs) are proposed for the new Weibull-Pareto distribution (NWPD) percentiles assuming truncated life tests at a pre-determined time. The minimum sample sizes essential to assert the specified percentile are calculated for a given consumer’s risk. The operating characteristic function values of the developed ASPs and producer’s risk are provided. A real data set related to the breaking stress of carbon fibers data are presented for illustration.

APPLICATIONS OF INVERSE WEIBULL RAYLEIGH DISTRIBUTION TO FAILURE RATES AND VINYL CHLORIDE DATA SETS

In this work, a new three parameter distribution called the Inverse Weibull Rayleigh distribution is proposed. Some of its statistical properties were presented. The PDF plot of Inverse Weibull Rayleigh distribution showed that it is good for modeling positively skewed and symmetrical datasets. The plot of the hazard function showed that the proposed distribution can fit datasets with bathtub shape. Method of maximum likelihood estimation was employed to estimate the parameters of the distribution, the estimators of the parameters of Inverse Weibull Rayleigh distribution is asymptotically unbiased and asymptotically efficient from the result of the simulation carried out. Applying the new distribution to a positively skewed Vinyl Chloride data set shows that the distribution performs better than Rayleigh, Generalized Rayleigh, Weibull Rayleigh, Inverse Weibull, Inverse Weibull Weibull, Inverse Weibull Inverse Exponential and Inverse Weibull Pareto distribution in fitting the data as it has the smallest AIC value. Also, applying the new distribution to a negatively skewed bathtub shape failure rates data shows that the distribution is a competitive model after Weibull Rayleigh and Inverse Weibull Weibull distributions in fitting the data because it has the third least AIC value.

The New Weibull-Pareto Distribution Stress-Strength Reliability for P(T

In this paper, the reliability formula of the stress-strength model is derived for probability of a component having strength X falling between two stresses T and Z, based on The New Weibull-Pareto Distribution with unknown parameter and known and common parameters and . Four methods for estimating the The New Weibull-Pareto parameters are discussed which are the Maximum Likelihood, Method of Moment, Least Square Method and Weighted Least Square Method, and the comparison between these estimations based on a simulation study by the mean square error criteria for each of the small, medium and large samples. The most important conclusion is that this comparison confirms that the performance of the maximum likelihood estimator works better for all experiments studied.

Estimation Methods for the New Weibull-Pareto Distribution: Simulation and Application

In this paper, we introduce the alternative methods to estimation for the new weibull-pareto distribution parameters. We discussed of point estimation and interval estimation for parameters of the new weibull-pareto distribution. We have also discussed the method of Maximum Likelihood estimation, the method of Least Squares estimation, the method of Weighted Least Squares estimation and the method of Maximum Product Spacing estimation. In addition, we discussed the raw moment of random variable X and the reliability functions (survival and hazard functions). Further, we compared between the results of the methods that have been discussed using Monte Carlo Simulation method and application study.

On Weibull-Pareto Distribution in Censored and Uncensored Data Structures

The Weibull distribution gives a flexible measurement that detailsthe probability distribution associated with the lifetime characteristics of a particular part orservice component. Itis commonly used to assess productreliability, analyze life data, and model failure times. It is a versatile distribution that can take on the characteristics of other types of distributions, based on the value of the shape parameter. Weibull-Pareto distribution has been introduced as a new type of application of the Weibull distribution. In this article, point and interval estimations for Weibull-Pareto distribution with censored and uncensored data are investigated. With real-time data applications, it is shown that Weibull-Pareto results are better against Exponential, Gamma, and Weibull distributions’ results.

Estimation of the Parameters of the New Weibull-Pareto Distribution Using Ranked Set Sampling

The method of maximum likelihood estimation based on ranked set sampling (RSS) and some of its modifications is used to estimate the unknown parameters of the new Weibull-Pareto distribution. The estimators are compared with the conventional estimators based on simple random sampling (SRS). The biases, mean squared errors, and confidence intervals are used to the comparison. The effect of the set size and number of cycles of the RSS schemes are addressed. Monte Carlo simulation is carried out by using R. The results showed that the RSS estimators are more efficient than their competitors using SRS.

Bayesian predictive analysis for Weibull-Pareto composite model with an application to insurance data

Aminzadeh and Deng, respectively provide Bayesian predictive models for Exponential-Pareto and Inverse Gamma-Pareto composite distributions which are one-parameter models. The purpose of this article is to develop an alternative Bayesian predictive model (two-parameter) which can be used to compute important risk measures that are not defined via the above predictive models. Bayesian predictive density for the Weibull-Pareto composite distribution is developed and is used to compute risk measures such as Value at Risk (VaR), Conditional Tail Expectation (CTE), Predictive Expectation (PE), Limited Predictive Expected value (LPE), Limited Predictive Variance (LPV), and Limited Predictive Tail-VaR (LPCTE). Accuracy of parameter estimates as well as the risk measures are assessed via simulation studies. It is shown that the informative Bayes estimates are consistently more accurate than ML and the non-informative Bayes estimates. Backtesting for the risk measures is performed and goodness-of-fit of Weibull-Pareto among other composite models to the Danish fire data is assessed.

Generalized Extreme Value-Pareto Distribution Function and Its Applications in Ocean Engineering

In this paper, we establish a generalized extreme Value-Pareto distribution model and derive an analytical expression of Weibull–Pareto distribution model. Based on a data sample of 26-year wave height, we adopt the new model to estimate the design wave height for 500, 700 and 1000-year return periods. Results show that the design wave height from Weibull–Pareto distribution is between that of the Weibull distribution and that of the Pearson-III distribution. For the 500-year return period design wave height, the results from the new model is 1.601% lower than those from the Weibull distribution and 1.319% higher than those from the Pearson-III distribution. The Weibull–Pareto distribution innovatively considers the fractal features, extreme-value statistics and the truncated data in the derivation process. Therefore, it is a more holistic and practical model for estimating the design parameters in marine and coastal environments.

The Weighted New Weibull Pareto Distribution Some Characteristics and Applications

The Weighted New Weibull Pareto Distribution Some Characteristics and Applications

Statistical inferences for new Weibull-Pareto distribution under an adaptive type-ii progressive censored data

In this paper, we obtain the maximum likelihood, Bayes and parametric bootstrap estimators for the parameters of a new Weibull-Pareto distribution (NWPD) and some lifetime indices such as reliability function S(t), failure rate h(t) function and coefficient of variation CV are obtained. The previous methods are studied in the case of an adaptive Type-II progressive censoring (Ada-T-II-Pro-C). Approximate confidence intervals (ACIs) of the unknown parameters are constructed based on the asymptotic normality of maximum likelihood estimators (MLEs). Bayes estimates and the symmetric credible intervals (CRIs) of the unknown quantities are calculated based on the Gibbs sampler within Metropolis– Hasting (M-H) algorithm procedure. The results of Bayes estimates are obtained under the consideration of the informative prior function with respect to the squared error loss (SEL) function. Two numerical examples are presented to illustrate the proposed methods, one of them is a simulated example and the other is a real life example. Finally, the performance of different Bayes estimates are compared with maximum likelihood (ML) and two parametric bootstrap estimates, through a Monte Carlo simulation study.

Robustness Study of the Sequential Testing Procedures for the New Weibull-Pareto Distribution

Robustness Study of the Sequential Testing Procedures for the New Weibull-Pareto Distribution