Estimation of the location and the scale parameters of Burr Type XII distribution

The aim of this paper is to estimate the location and the scale parameters of Burr Type XII distribution. For this purpose, different estimation methods, namely, maximum likelihood (ML), modified maximum likelihood (MML), least squares (LS) and method of moments (MM) are used. The performances of these estimation methods are compared via Monte-Carlo simulation study under different sample sizes and parameter settings. At the end of the study, the wind speed data set and the annual flow data sets are analyzed for illustration of the modeling performance of Burr Type XII distribution

The Burr XII modified Weibull distribution: model, properties and applications

A new distribution called Burr XII modified Weibull (BXIIMW or BMW) distribution is presented and its properties explored. This new distribution contains several new and well known sub-models, including Burr-Weibull, Burr-exponential, Burr-Rayleigh, Burr XII, Lomax modified Weibull, Lomax-Weibull, Lomax-exponential, Lomax-Rayleigh, Lomax, Weibull, Rayleigh, and exponential distributions. Some structural properties of the proposed distribution including the shapes of the density and hazard rate functions, moments, conditional moments, moment generating function, skewness and kurtosis are presented. Mean deviations, Lorenz and Bonferroni curves, R\'enyi entropy and the distribution of the order statistics are given. The maximum likelihood estimation technique is used to estimate model parameters and finally applications of the model to real data sets are presented to illustrate the usefulness of the proposed distribution

Some Estimation Methods for the Shape Parameter and Reliability Function of Burr Type XII Distribution / Comparison Study

Burr type XII distribution plays an important role in reliability modeling, risk analyzing and process capability estimation. The choice of the best estimation method is one of the goals in estimating parameters of the distribution. The main aim of this paper is to obtain and compare the classical "maximum likelihood and uniformly minimum variance unbiased" estimators and the Bayesian estimators of the shape parameter, ???? and reliability function based on a complete sample when the other shape parameter, ? known. The Bayes estimators are obtained under non-informative priors "Jeffrey’s prior, modified and extension of Jeffrey’s prior" as well as under informative gamma prior based on different symmetric and asymmetric loss functions "squared error, quadratic, LINEX, precautionary and entropy". The Monte Carlo experiment was performed under a wide range of cases and sample size. The estimates of the unknown shape parameter were compared by employing the mean square errors and the estimates of reliability function were compared by employing the integrated mean squared error.   Keywords: Burr type XII distribution; Maximum likelihood estimator; Uniformly Minimum Variance Unbiased estimator; Bayes estimators; non-informative Prior; informative Prior; Squared error loss function; quadratic loss function; LINEX loss function; Precautionary loss function; Entropy Loss function; Mean squared error; integrated mean squared error

Bayesian Inference for Concomitants based on Weibull Subfamily of Morgenstern Family Under Generalized Order Statistics

In this paper, for Weibull subfamily of Morgenstern family, the joint density of the concomitants of generalized order statistics (GOS's) is used to obtain the maximum likelihood estimates (MLE) and Bayes estimates for the distribution parameters. Applications of these results for concomitants of order statistics are presented

Finding appropriate loss distributions to insurance data Case study of Kenya (2010-2014)

A Research project submitted in partial fulfillment of the requirements for the degree of Bachelor of Business Science in Actuarial Science at Strathmore UniversityObtaining the total amount of claims for a specific period is a vital part of the daily work of insurance companies. This will help in various ways the management in running the company (Jouravlev, 2009). For instance, the insurance company will be able to calculate the premium for a type of policy by the use of the claim experience. Moreover, it will be able to reserve a certain amount of money to cover the cost of future claims. Premium computation and Reserving are not the only reasons for which loss distributions are needed. Loss distributions are also utilised in reviewing reinsurance arrangements and also in testing for solvency. This explicitly highlights the importance of loss distribution in the insurance industry. This paper therefore aims to determine the most suitable loss distributions for various sort of insurance contracts being general or life insurance in the Kenyan market industry. The following distributions will be compared: the exponential distribution, the Pareto distribution, the Generalised Pareto distribution, the lognormal distribution, the Weibull distribution & the Burr distribution. We will see how these distributions can be tailored in order to suit the observed data. Afterwards, a test of goodness-of-fit will be used to determine the level of robustness of the distribution in fitting the given data. The loss distributions will also be used in order the probabilities of future events happening

On Maximum Likelihood Estimation for Left Censored Burr Type III Distribution

<p>Burr type III is an important distribution used to model the failure time data. The paper addresses the problem of estimation of parameters of the Burr type III distribution based on maximum likelihood estimation (MLE) when the samples are left censored. As the closed form expression for the MLEs of the parameters cannot be derived, the approximate solutions have been obtained through iterative procedures. An extensive simulation study has been carried out to investigate the performance of the estimators with respect to sample size, censoring rate and true parametric values. A real life example has also been presented. The study revealed that the proposed estimators are consistent and capable of providing efficient results under small to moderate samples.</p

On The Weighted BurrXII Distribution: Theory and Practice

We take an in-depth look at the weighted Burr-XII distribution. This distribu-tion generalizes Burr-XII, Lomax, and log-logistic distributions. We discuss the dis-tributional characteristics of the probability density function, the failure rate function,and mean residual lifetime of this distribution. Moreover, we obtain various statisti-cal properties of this distribution such as moment generating function, entropies, meandeviations, order statistics and stochastic ordering. The estimation of the distributionparameters via maximum likelihood method and the observed Fisher information ma-trix are discussed. We further employ a simulation study to investigate the behavior ofthe maximum likelihood estimates (MLEs). A test concerning the existence of size-biasin the sample is provided. In the end, a real data is presented and is analyzed usingthis distribution along with some existing distributions for illustrative purposes

On Optimal Designs of Some Censoring Schemes

The main objective of this paper  is to explore suitability of some entropy-information measures for introducing a new optimality censoring criterion and to apply it to some censoring schemes from some underlying life-time models.  In addition, the  paper investigates four related issues namely; the  effect of the parameter of parent distribution on optimal scheme, equivalence of schemes based on Shannon and Awad sup-entropy measures, the conjecture that the optimal scheme is one stage scheme, and  a conjecture by Cramer and Bagh (2011) about Shannon minimum and maximum schemes when parent distribution is reflected power. Guidelines for designing an optimal censoring plane are reported together with theoretical and numerical results and illustrations