• Communications for Statistical Applications and Methods
• /
• v.22 no.4
• /
• pp.333-348
• /
• 2015

In this paper, we study a generalization of the modified Weibull distribution. The generalization follows the recent work of Cordeiro et al. (2013) and is based on a class of exponentiated generalized distributions that can be interpreted as a double construction of Lehmann. We introduce a class of exponentiated generalized modified Weibull (EGMW) distribution and provide a list of some well-known distributions embedded within the proposed distribution. We derive some mathematical properties of this class that include ordinary moments, generating function and order statistics. We propose a maximum likelihood method to estimate model parameters and provide simulation results to assess the model performance. Real data is used to illustrate the usefulness of the proposed distribution for modeling reliability data.

• Communications for Statistical Applications and Methods
• /
• v.30 no.2
• /
• pp.191-213
• /
• 2023

Unit distributions are frequently used in probability theory and statistics to depict meaningful variables having values between zero and one. Using convenient transformation, the unit inverse exponentiated weibull (UIEW) distribution, which is equally useful for modelling data on the unit interval, is proposed in this study. Quantile function, moments, incomplete moments, uncertainty measures, stochastic ordering, and stress-strength reliability are among the statistical properties provided for this distribution. To estimate the parameters associated to the recommended distribution, well-known estimation techniques including maximum likelihood, maximum product of spacings, least squares, weighted least squares, Cramer von Mises, Anderson-Darling, and Bayesian are utilised. Using simulated data, we compare how well the various estimators perform. According to the simulated outputs, the maximum product of spacing estimates has lower values of accuracy measures than alternative estimates in majority of situations. For two real datasets, the proposed model outperforms the beta, Kumaraswamy, unit Gompartz, unit Lomax and complementary unit weibull distributions based on various comparative indicators.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.30 no.11 s.254
• /
• pp.1417-1424
• /
• 2006

In order to evaluate variation of fatigue life of mechanical components including engineering plastics, it is important to estimate probabilistic strain-life curves to accurately define the variation of fatigue characteristics. This paper intends to provide new assessment of P-$\varepsilon$-N (probabilistic strain-life curves) for considering the variation of fatigue characteristics in polyacetal. The fatigue strain controlled tests were conducted under constant 50% humidity and room temperature condition by a universal testing machine at strain ratio, R=0. A practical procedure is introduced to evaluate probabilistic strain-life curves. Three probabilistic distributions were used for generating P-$\varepsilon$-N curves such as normal, 2-parameter and 3-parameter Weibull. In this study, 3-parameter Weibull distribution was found to be most appropriate among assumed distributions when the probability distributions of the fatigue characteristic were examined using chi-square and Kolmogorov-Smirnov test. The more appropriate P-$\varepsilon$-N curves for these materials are generated by the proposed method considering 3-parameter Weibull distribution.

• Journal of the Korean Data and Information Science Society
• /
• v.15 no.3
• /
• pp.593-603
• /
• 2004

We consider the problem of estimating the scale parameter of the Weibull distribution based on multiply Type-II censored samples. We propose two estimators by using the approximate maximum likelihood estimation method for Weibull and extreme value distributions. The proposed estimators are compared in the sense of the mean squared error.

• Communications of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.1335-1352
• /
• 2019

In this article, a new family of lifetime distributions by adding two additional parameters is introduced. The new family is called, the logarithmic Kumaraswamy family of distributions. For the proposed family, explicit expressions for some mathematical properties are derived. Maximum likelihood estimates of the model parameters are also obtained. This method is applied to develop a new lifetime model, called the logarithmic Kumaraswamy Weibull distribution. The proposed model is very flexible and capable of modeling data with increasing, decreasing, unimodal or modified unimodal shaped hazard rates. To access the behavior of the model parameters, a simulation study has been carried out. Finally, the potentiality of the new method is proved via analyzing two real data sets.

• Communications for Statistical Applications and Methods
• /
• v.23 no.5
• /
• pp.399-409
• /
• 2016

Many of studies have suggested the modifications on Weibull distribution to model the non-monotone hazards. In this paper, we combine two cumulative hazard functions and propose a new modified Weibull distribution function. The newly suggested distribution will be named as a new flexible Weibull distribution. Corresponding hazard function of the proposed distribution shows flexible (monotone or non-monotone) shapes. We study the characteristics of the proposed distribution that includes ageing behavior, moment, and order statistic. We also discuss an estimation method for its parameters. The performance of the proposed distribution is compared with existing modified Weibull distributions using various types of hazard functions. We also use real data example to illustrate the efficiency of the proposed distribution.

• Journal of Korean Society of Forest Science
• /
• v.90 no.2
• /
• pp.176-183
• /
• 2001

Loblolly pine (Pinus taeda L.) is the most economically important timber producing species in the southern United States. Much attention has been given to predicting diameter distributions for the solution of multiple-product yield estimates. The three-parameter Weibull diameter distribution yield prediction systems were developed for loblolly pine plantations. A parameter recovery procedure for the Weibull distribution function based on four percentile equations was applied to develop diameter distribution yield prediction models. Four percentiles (0th, 25th, 50th, 95th) of the cumulative diameter distribution were predicted as a function of quadratic mean diameter. Individual tree height prediction equations were developed for the calculation of yields by diameter class. By using individual tree content prediction equations, expected yield by diameter class can be computed. To reduce rounding-off errors, the Weibull cumulative upper bound limit difference procedure applied in this study shows slightly better results compared with upper and lower bound procedure applied in the past studies. To evaluate this system, the predicted diameter distributions were tested against the observed diameter distributions using the Kolmogorov-Smirnov two sample test at the ${\alpha}$=0.05 level to check if any significant differences existed. Statistically, no significant differences were detected based on the data from 516 evaluation data sets. This diameter distribution yield prediction system will be useful in loblolly pine stand structure modeling, in updating forest inventories, and in evaluating investment opportunities.

• Journal of Applied Reliability
• /
• v.14 no.3
• /
• pp.182-190
• /
• 2014

This paper presents new practical accelerated life test plans with different censoring times at three levels of stress for Weibull and lognormal lifetime distributions, respectively. The proposed plans are compared with the corresponding two-level statistically optimal plans and three-level compromise and practical plans. Computational results indicate that new practical plans have been more precise and effective than the existing three-level plans under a constraint of total testing time. In addition, a procedure to determine useful ALT plans is illustrated with a numerical example.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.33 no.10
• /
• pp.1144-1150
• /
• 2009

This paper investigates the feasibility of the Bayesian discrete time approximation method to estimate the parameters of Weibull distributions of failures for two non-identical components connected in series system. A Bayesian model based on the discrete time approximation method is formulated to infer the Weibull parameters of two non-identical components with the failure data of the virtual tests. The study of this paper comes to a conclusion that the method is feasible only for some special cases under the given constraints on the concerned parameters.

• Journal of the Korean Data and Information Science Society
• /
• v.25 no.6
• /
• pp.1569-1579
• /
• 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.