A near-maximum is an observation which falls within a distance a of the maximum observation in an independent and identically distributed sample of size n. Subject to some conditions on the tail thickness of the population distribution, the number Kn(a) of nearmaxima is known to converge in probability to one or infinity, or in distribution to a shifted geometric law. In this paper we show that...

Neonatal Mortality Rate (NMR) can be defined as the number of newborn deaths’ aged 0 to 28 days. The most significant factor influenced NMR is low birth weight of newborn babies approximately 48%, followed by asphyxia 37% and sepsis 32.5%. This paper deploys a Burr XII distribution to model the Non-Normal Neonatal Weight data. The parameters of the fitted Burr XII distribution are estimated usi...

This paper deals with Bayesian inference and prediction problems of the Burr type XII distribution based on progressive first failure censored data. We consider the Bayesian inference under a squared error loss function. We propose to apply Gibbs sampling procedure to draw Markov Chain Monte Carlo (MCMC) samples, and they have in turn, been used to compute the Bayes estimates with the help of i...

The Burr Type XII distribution is one of the systems of continuous distributions and is widely known because the distribution includes the characteristics of various well known distributions such as Weibull and gamma distributions. Maximum likelihood estimation (MLE) has been a common method in estimating model parameters. An alternative method that is the expectation-maximization (EM) algorith...

This paper obtains Lorenz ordering relationships among order statistics from log-logistic samples of possibly different sizes. Some results extend other families including the Lomax, Burr III and Burr XII distributions.

In general, classical methods such as maximum likelihood (ML) and least squares (LS) estimation methods are used to estimate the shape parameters of the Burr XII distribution. However, these estimators are very sensitive to the outliers. To overcome this problem we propose alternative robust estimators based on the M-estimation method for the shape parameters of the Burr XII distribution. We pr...

The Burr type III distribution allows for a wider region for the skewness and kurtosis plane, which covers several distributions including the log-logistic, and theWeibull and Burr type XII distributions. However, outliersmay occur in the data set. The robust regressionmethod such as an M-estimator with symmetric influence function has been successfully used to diminish the effect of outliers o...