On the Three-Parameter Burr Type XII Distribution and its Application to Heavy Tailed Lifetime Data

This paper identifies the characteristics of three-parameter Burr Type XII distribution and discusses its utility in survivorship applications. It addresses the problem of estimating the three-parameter Burr XII distribution and its doubly truncated version. The results are applied on a real dataset by fitting the distribution to the survival time of breast cancer patients in the Gaza Strip. These data are known to have a heavy tailed distribution since patients in this area received different protocols of treatments in different levels of hospitals locally and abroad. The findings indicated that the estimates of the parameters of the truncated distribution are more efficient than those obtained from the original distribution since the distribution is heavy tailed and involves many highly extreme observations

Application of Burrxii-Dal and Weibull-Dal Distribution: A Case Study of Wheat Yield in Multan Pakistan

Background Statistical analysis is highly dependent on the Probability distribution of the data and new models are most important part for the expansion of this field. Burr-XII DAL (BDAL) and Weibull-DAL (WDAL) distribution with five parameters are used to analysis the distribution and to predict the yield and growth rate of different products. Objective The purpose of the study is to determine the effectiveness of the application of modified BURRXII-DAL and WEIBULL-DAL distribution for the analysis of the wheat yield in Multan, Pakistan by estimating their maximum likelihood. Methodology The study involves the comparative analysis of Burr-XII DAL (BDAL) and Weibull-DAL (WDAL) distribution with other distribution models including Beta exponentiated Nadarajah Haghighi (BENH), Kumaraswamy Nadarajah Haghighi, exponentiated generalized Nadarajah Haghighi and modified Nadarajah Haghighi (MNH). The properties of Burr-XII DAL (BDAL) and Weibull-DAL (WDAL) analyzed through the R package and software to determine MLE, standard errors and W∗, A∗, K-S, p-value, AIC, BIC and l ̂along with Akaike information criteria (AIC) and Bayesian information criteria (BIC). Conclusion The study concluded that modified propose Burr-XII DAL (BDAL) and Weibull-DAL (WDAL) are effective alternative models for the analysis of the distribution due to their high reliability and maximum likelihood value for the data make it reliable for the analysis of the real-life dat

On the Burr XII-moment Exponential Distribution

In this study, a new flexible lifetime model called Burr XII moment exponential (BXII-ME) distribution is introduced. We derive some of its mathematical properties including the ordinary moments, conditional moments, reliability measures and characterizations. We employ different estimation methods such as the maximum likelihood, maximum product spacings, least squares, weighted least squares, Cramer-von Mises and Anderson-Darling methods for estimating the model parameters. We perform simulation studies on the basis of the graphical results to see the performance of the above estimators of the BXII-ME distribution. We verify the potentiality of the BXII-ME model via monthly actual taxes revenue and fatigue life applications

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

RELIABILITY OF OPTIONS MARKETS FOR CROP REVENUE INSURANCE RATING

Revenue insurance, only recently introduced for major crops in the U.S., has captured a considerable share of the multiple-peril insurance market. This study evaluates the predictive reliability of using price distributions inferred from options markets to rate revenue insurance products. We find for periods early in the crop growing season that price distributions inferred from options trades offer greater reliability than distributions based on historical futures trades. Options-based price distributions should receive further consideration in crop revenue insurance rating, but current administrative constraints must be considered.Risk and Uncertainty,

A Guide to the Dagum Distributions

In a series of papers in the 1970s, Camilo Dagum proposed several variants of a new model for the size distribution of personal income. This Chapter traces the genesis of the Dagum distributions in applied economics and points out parallel developments in several branches of the applied statistics literature. It also provides interrelations with other statistical distributions as well as aspects that are of special interest in the income distribution eld, including Lorenz curves and the Lorenz order and inequality measures. The Chapter ends with a survey of empirical applications of the Dagum distributions, many published in Romance language periodicals.

Using epidemic prevalence data to jointly estimate reproduction and removal

This study proposes a nonhomogeneous birth--death model which captures the dynamics of a directly transmitted infectious disease. Our model accounts for an important aspect of observed epidemic data in which only symptomatic infecteds are observed. The nonhomogeneous birth--death process depends on survival distributions of reproduction and removal, which jointly yield an estimate of the effective reproduction number $R(t)$ as a function of epidemic time. We employ the Burr distribution family for the survival functions and, as special cases, proportional rate and accelerated event-time models are also employed for the parameter estimation procedure. As an example, our model is applied to an outbreak of avian influenza (H7N7) in the Netherlands, 2003, confirming that the conditional estimate of $R(t)$ declined below unity for the first time on day 23 since the detection of the index case.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS270 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org