Bayesian life test sampling plans for the two parameter exponential distribution

In this paper we consider the determination of Bayesian life test acceptance sampling plans for finite lots when the underlying lifetime distribution is the two parameter exponential. It is assumed that the prior distribution is the natural conjugate prior, that the costs associated with the actions accept and reject are known functions of the lifetimes of the items, and that the cost of testing a sample is proportional to the duration of the test. Type 2 censored sampling is considered where a sample of size n is observed only until the rth failure occurs and the decision of whether to accept or reject the remainder of the lot is made on the basis of the r observed lifetimes. Obtaining the optimal sample size and the optimal censoring number are difficult problems when the location parameter of the distribution is restricted to be non-negative. The case when the positivity restriction on the location parameter is removed has been investigated. An example is provided for illustration.     

Asymptotic Distributions of the Generalized Range,Midrange, Extremal Quotient,and Extremal Product,with a Comparison Study

Necessary and sufficient conditions for the weak convergence of the generalized range, midrange, extremal quotient, and extremal product are obtained. The classes of possible non degenerate limit distribution functions of these simple statistics are characterized. Comparison study between these statistics with some examples for the most important distribution functions are given.     

Bootstrap Method for Order Statistics and Modeling Study of the Air Pollution

In this article, the block maxima (BM) and the peak over threshold (POT) methods are used to model the air pollution. A simulation technique is suggested to choose a suitable threshold value. The validity of the estimated models is checked by the Kolmogorov–Smirnov (K-S) test. A new efficient approach for modeling extreme values is suggested. Finally, the inconsistency and weak consistency of bootstrapping central and intermediate order statistics for an appropriate choice of re-sample size are investigated.     

Prediction bounds for the burr model

Given a type 2 censored sample from the Burr life time distribution, Bayesian prediction bounds are derived for future observations. An approximate Bayesian method has been used to simplify the computation of the prediction bounds. Numerical examples are used to illustrate the procedures.     

Hormone profiles,body mass index and aging male symptoms: results of the Androx Vienna Municipality study

Aging in the male is accompanied by steroid hormonal decline, and men may develop symptoms associated with hypogonadism. Increased awareness of ‘andropause’ in recent years has led to greater demand for hormonal assessments, resulting in a rising burden for health economics. We conducted a cross-sectional study to define men at risk for hypogonadism, in whom further hormonal investigation should be performed.

We examined 664 blue-collar workers aged 40–60 years at their workplace and determined hormonal status and body mass index (BMI). Men with an abnormal urogenital status and those on medication that might affect endocrine status were excluded from the study. All participants completed the validated Aging Male Symptom (AMS) questionnaire and obtained scores for psychological symptoms, somatovegetative symptoms, and sexual symptoms.

Multiple logistic regression analyses revealed a significantly increased risk (represented by the odds ratio) of psychological symptoms for men with low levels of testosterone and/or bioavailable testosterone (BAT). Increased BMI as well as low testosterone levels and/or low BAT levels raised the risk of somatovegetative symptoms. Each decrease of BAT by 1?ng/ml caused an approximately 1.8-fold increase of the risk (odds ratio?=?1.832, p?=?0.005). Additional independent risk factors were increased age and low luteinizing hormone (LH) level. Men aged 55 years with BMI >?28?kg/m² and with somatovegetative symptoms and moderate or severe psychological symptoms had a 7.2-fold increase in the risk of a BAT level <?1.5?ng/ml compared to men without these risk factors (p <?0.001). Sensitivity and specificity were 75% and 71%, respectively.

The AMS score combined with age and BMI provides an easy and convenient method to identify men with probable androgen deficiency who require hormonal assessment.     

Bayesian one-sample prediction of future observations under Pareto distribution

Suppose that the length of time in years for which a business operates until failure has a Pareto distribution. Let t ₁?t ₂?t _r denote the survival lifetimes of the first r of a random sample of n businesses. Bayesian predictions are to be made on the ordered failure times of the remaining (n???r) businesses, using the conditional probability function. Numerical examples are given to illustrate our results.