• Title/Summary/Keyword: Inverse Weibull distribution

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Bayesian and maximum likelihood estimation of entropy of the inverse Weibull distribution under generalized type I progressive hybrid censoring

  • Lee, Kyeongjun
    • Communications for Statistical Applications and Methods
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    • v.27 no.4
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    • pp.469-486
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    • 2020
  • Entropy is an important term in statistical mechanics that was originally defined in the second law of thermodynamics. In this paper, we consider the maximum likelihood estimation (MLE), maximum product spacings estimation (MPSE) and Bayesian estimation of the entropy of an inverse Weibull distribution (InW) under a generalized type I progressive hybrid censoring scheme (GePH). The MLE and MPSE of the entropy cannot be obtained in closed form; therefore, we propose using the Newton-Raphson algorithm to solve it. Further, the Bayesian estimators for the entropy of InW based on squared error loss function (SqL), precautionary loss function (PrL), general entropy loss function (GeL) and linex loss function (LiL) are derived. In addition, we derive the Lindley's approximate method (LiA) of the Bayesian estimates. Monte Carlo simulations are conducted to compare the results among MLE, MPSE, and Bayesian estimators. A real data set based on the GePH is also analyzed for illustrative purposes.

Development of accelerated life test method for mechanical components using Weibull-IPL(Inverse Power Law) model (와이블-역승법을 이용한 기계류부품의 가속시험 방법 개발)

  • Lee, Geun-Ho;Kim, Hyoung-Eui;Kang, Bo-Sik
    • Proceedings of the KSME Conference
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    • 2003.04a
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    • pp.445-450
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    • 2003
  • This study was performed 10 develop the accelerated life test method using Weibull-IPL(Inverse Power Law) model for mechanical components. Weibull-IPL model is concerned with determining the assurance life with confidence level and the accelerated life test time From the relation of weibull distribution factors and confidence limit, the testing times on the no number of failure acceptance criteria arc determined. The mechanical components generally represent wear and fatigue characteristics as a failure mode. IPL based on the cumulative damage theory is applied effectively the mechanical components to reduce the testing time and to achieve the accelerating test conditions. As the actual application example, accelerated life test method of agricultural tractor transmission was described. Life distribution of agricultural tractor transmission was supposed to follow Weibull distribution and life test time was calculated under the conditions of average life (MTBF) 3,000 hours and 90% confidence level for one test sample. According to IPL, because test time call be shorten in case increase test load test time could be reduced by 482 hours when we put the load 1.1 times of rated load than 0.73 times of rated load that is equivalent load calculated by load spectrum of the agricultural tractor. This time, acceleration coefficient was 11.7.

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ON CHARACTERIZATIONS OF CONTINUOUS DISTRIBUTIONS BY CONDITIONAL EXPECTATIONS OF UPPER RECORD VALUES

  • Jin, Hyun-Woo;Lee, Min-Young
    • Journal of the Chungcheong Mathematical Society
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    • v.25 no.3
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    • pp.501-505
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    • 2012
  • In this paper, general classes of continuous distributions are characterized by considering the conditional expectations of functions of upper record statistics. The specific distribution considered as a particular case of the general class of distribution are Exponential, Exponential Power(EP), Inverse Weibull, Beta Gumbel, Modified Weibull(MW), Weibull, Pareto, Power, Singh-Maddala, Gumbel, Rayleigh, Gompertz, Extream value 1, Beta of the first kind, Beta of the second kind and Lomax.

Power Investigation of the Entropy-Based Test of Fit for Inverse Gaussian Distribution by the Information Discrimination Index

  • Choi, Byungjin
    • Communications for Statistical Applications and Methods
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    • v.19 no.6
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    • pp.837-847
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    • 2012
  • Inverse Gaussian distribution is widely used in applications to analyze and model right-skewed data. To assess the appropriateness of the distribution prior to data analysis, Mudholkar and Tian (2002) proposed an entropy-based test of fit. The test is based on the entropy power fraction(EPF) index suggested by Gokhale (1983). The simulation results report that the power of the entropy-based test is superior compared to other goodness-of-fit tests; however, this observation is based on the small-scale simulation results on the standard exponential, Weibull W(1; 2) and lognormal LN(0:5; 1) distributions. A large-scale simulation should be performed against various alternative distributions to evaluate the power of the entropy-based test; however, the use of a theoretical method is more effective to investigate the powers. In this paper, utilizing the information discrimination(ID) index defined by Ehsan et al. (1995) as a mathematical tool, we scrutinize the power of the entropy-based test. The selected alternative distributions are the gamma, Weibull and lognormal distributions, which are widely used in data analysis as an alternative to inverse Gaussian distribution. The study results are provided and an illustrative example is analyzed.

Default Bayesian testing for the equality of shape parameters in the inverse Weibull distributions

  • Kang, Sang Gil
    • Journal of the Korean Data and Information Science Society
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    • v.25 no.6
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    • pp.1569-1579
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    • 2014
  • This article deals with the problem of testing for the equality of the shape parameters in two inverse Weibull distributions. We propose Bayesian hypothesis testing procedures for the equality of the shape parameters under the noninformative prior. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

A Condition Based Maintenance Model for Systems with Weibull Distributed Deterioration (와이블 분포로 열화하는 시스템의 상태에 기초한 정비모형)

  • Kong, Myung Bock;Park, Il Gwang
    • Journal of Korean Institute of Industrial Engineers
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    • v.33 no.1
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    • pp.70-75
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    • 2007
  • This paper discusses condition based preventive replacement for deteriorating systems. The system continuouslydeteriorates in time and fails at any deterioration level which is always monitored, It is replaced at failure or atsome deteriorated level preventively before failure. The deterioration process is represented by a Weibulldistribution with a time-linear scale parameter. The cost rate function is formed considering replacement costand opportunity loss cost and deterioration dependent failure distribution, If the system has an increasingdeterioration dependent failure rate, the optimal deterioration level for preventive replacement can be determinedfrom minimizing the cost rate. An illustrative example is given for a Weibull deterioration dependent failuredistribution.

Kernel Inference on the Inverse Weibull Distribution

  • Maswadah, M.
    • Communications for Statistical Applications and Methods
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    • v.13 no.3
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    • pp.503-512
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    • 2006
  • In this paper, the Inverse Weibull distribution parameters have been estimated using a new estimation technique based on the non-parametric kernel density function that introduced as an alternative and reliable technique for estimation in life testing models. This technique will require bootstrapping from a set of sample observations for constructing the density functions of pivotal quantities and thus the confidence intervals for the distribution parameters. The performances of this technique have been studied comparing to the conditional inference on the basis of the mean lengths and the covering percentage of the confidence intervals, via Monte Carlo simulations. The simulation results indicated the robustness of the proposed method that yield reasonably accurate inferences even with fewer bootstrap replications and it is easy to be used than the conditional approach. Finally, a numerical example is given to illustrate the densities and the inferential methods developed in this paper.

New generalized inverse Weibull distribution for lifetime modeling

  • Khan, Muhammad Shuaib;King, Robert
    • Communications for Statistical Applications and Methods
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    • v.23 no.2
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    • pp.147-161
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    • 2016
  • This paper introduces the four parameter new generalized inverse Weibull distribution and investigates the potential usefulness of this model with application to reliability data from engineering studies. The new extended model has upside-down hazard rate function and provides an alternative to existing lifetime distributions. Various structural properties of the new distribution are derived that include explicit expressions for the moments, moment generating function, quantile function and the moments of order statistics. The estimation of model parameters are performed by the method of maximum likelihood and evaluate the performance of maximum likelihood estimation using simulation.

Higher Order Moments of Record Values From the Inverse Weibull Lifetime Model and Edgeworth Approximate Inference

  • Sultan, K.S.
    • International Journal of Reliability and Applications
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    • v.8 no.1
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    • pp.1-16
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    • 2007
  • In this paper, we derive exact explicit expressions for the triple and quadruple moments of the lower record values from inverse the Weibull (IW) distribution. Next, we present and calculate the coefficients of the best linear unbiased estimates of the location and scale parameters of IW distribution (BLUEs) for different choices of the shape parameter and records size. We then use the higher order moments and the calculated BLUEs to compute the mean, variance, and the coefficients of skewness and kurtosis of certain linear functions of lower record values. By using the coefficients of the skewness and kurtosis, we develop approximate confidence intervals for the location and scale parameters of the IW distribution using Edgeworth approximate values and then compare them with the corresponding intervals constructed through Monte Carlo simulations. Finally, we apply the findings of the paper to some simulated data.

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MOMENTS OF LOWER GENERALIZED ORDER STATISTICS FROM DOUBLY TRUNCATED CONTINUOUS DISTRIBUTIONS AND CHARACTERIZATIONS

  • Kumar, Devendra
    • Journal of the Chungcheong Mathematical Society
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    • v.26 no.3
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    • pp.441-451
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    • 2013
  • In this paper, we derive recurrence relations for moments of lower generalized order statistics within a class of doubly truncated distributions. Inverse Weibull, exponentiated Weibull, power function, exponentiated Pareto, exponentiated gamma, generalized exponential, exponentiated log-logistic, generalized inverse Weibull, extended type I generalized logistic, logistic and Gumble distributions are given as illustrative examples. Further, recurrence relations for moments of order statistics and lower record values are obtained as special cases of the lower generalized order statistics, also two theorems for characterizing the general form of distribution based on single moments of lower generalized order statistics are given.