Comparison of two weibull distributions under random censoring

The two-sample problem for comparing Weibull scale parameters is studied for randomly censored data. Three different test statistics are considered and their asymptotic properties are established under a sequence of local alternatives, It is shown that both the test statistic based on the mlefs (maximum likelihood estimators) and the likelihood ratio test are asymptotically optimum. The third statistic based only on the number of failures is not, Asymptotic relative efficiency of this statistic is obtained and its numerical values are computed for uniform and Weibull censoring, Effects of uniform random censoring on the censoring level of the experiment are illus¬trated, A direct proof for the joint asymptotic normality of the mlefs of the shape and the scale parameters is also given     

Humerical. Results concerning the mle of an exponential parameter used in life testing

It was previously shown that the maximum likelihood estimator 0 of the scale parameter of the exponential distribution is asymptotically normal for type-I censoring. Applicability of the asymptotic normality results for finite samples is studied here by computer simulation for several different normalizing factors and for various levels of censoring. The use of the asymptotic results in statistical problems is illustrated by an example     

Is consanguinity an impediment to child development?

Marriages between blood relatives—also known as consanguineous unions—are widespread in North Africa, Central and West Asia, and South Asia. Researchers have suggested that consanguinity has adverse effects on child development, but assessing its impact is not straightforward, as the decision to marry a relative might be endogenous to other socio-economic factors. Using a unique data set collected in rural Pakistan, this paper assesses the extent to which consanguinity is linked to children’s cognitive and physical development. It exploits grandfathers’ land ownership (current and past) and maternal grandparent mortality to identify the effect of endogenous consanguinity on child development. Children born into consanguineous unions have lower cognitive scores, lower height-for-age, and a higher likelihood of being severely stunted. More importantly, adverse effects are greater after accounting for the endogeneity of consanguinity, suggesting that impacts on child development are substantial, and likely to be larger than suggested in previous studies.     

An estimator for the scale parameter of the two parameter weibull distribution for type i singly right-censored data

For type I censoring, in addition to the failure times, the number failures is also observed as part of the data. Using this feature of type I singly right-censored data a simple estimator is obtained for the scale parameter of the two parameter Weibull distribution. The exact mean and variance of the estimator are derived and computed for finite sample sizes. Its limiting properties such as asymptotic normality and asymptotic relative efficiency are obtained. The estimator has high efficiency for moderate and heavy censoring. Its use is illustrated by means of an example.