##### Mathematical Programming for Statistical Inference

Abeer M. M. Elrefaey, Ramadan Hamid, Elham A. Ismail, Safia M. Ezzat

Asian Journal of Probability and Statistics, Page 1-8
DOI: 10.9734/ajpas/2018/v1i124495

The study is concerned with the transforming theoretical Mathematical models into applied Mathematical programming models that are easy to handle and use. These Mathematical programming models can be applied and used in statistical inference, which used in many applied fields, for example, quality control and its application. The aim of this paper is to suggest two mathematical programming models for hypotheses tests, which make a balance between the high power (1-β), and the probability of a type I error, significance (), of the test. The paper introduces a simulation study to evaluate the performance of the two suggested mathematical programming models for tests hypotheses. The two suggested mathematical programming models solved with different sample sizes and different level of significance. The suggested models calculate the critical values which determine the rejection region exactly and the results are easy to interpret clearly. Then the conclusion for the suggested mathematical programming models makes balance between the power and the significance.

##### Measuring the Cost for Some Single Channel Waiting Line Models

Doaa A. Ali, Elham A. Ismail, Lobna E. AL-Tayeb

Asian Journal of Probability and Statistics, Page 1-10
DOI: 10.9734/ajpas/2018/v1i124499

Queuing models applications are centered on the question of finding the ideal level of services, waiting times and queue lengths. The aim of this study is to measure the cost for three models and compare the cost for the three single channel waiting line models instead of finding the ideal level of services, waiting times and queue lengths which calculated in many studies.  Each model depends on two important parameters arrival rate (λ) and service rate (μ) which followed different distributions.  The cost for the three single channel waiting line models is calculated when arrival rate (λ) is followed Poisson distribution and service rate (μ) is followed different distributions. The objective for the waiting line models is to minimize total expected costs by minimize the sum of service costs and waiting costs. Therefore, the study concerned with changing the distribution of the service rate (μ) and examining its impact on cost. This choice was made to emphasize the basic idea of the study (there is a relationship between the service rate distribution and the cost). The study results showed that there is a relationship between the service rate   distribution and the cost.

##### Some Characterizations of Transmuted Modified Burr III Distribution

Asian Journal of Probability and Statistics, Page 1-9
DOI: 10.9734/ajpas/2018/v1i124498

In this paper, Transmuted Modified Burr III (TMBIII) distribution (Ali and Ahmad; 2015) is characterized through  (i) ratio of truncated moments; (ii) doubly truncated moments; (iii) hazard rate function; (iv) reverse hazard rate function and (v) elasticity function. The applications of characterizations of TMBIII distribution will be beneficial for scientists in different areas of science.

##### Spectrum of Sex Ratios in Denmark

Johan Fellman

Asian Journal of Probability and Statistics, Page 1-7
DOI: 10.9734/ajpas/2018/v1i124502

The sex ratio (SR) is usually defined as the number of males per 100 females within an area or, as in this study, the proportion of males among all births (PM). It has been observed that among newborns, there is typically a slight excess number for boys compared to girls. Consequently, the SR becomes greater than 100, which is around 106 in number, and the chance of new born males is around 0.515. Attempts have been made to identify the factors those are influencing the level of the PM. Previous researches stated that where prenatal losses are low, as in the Western countries, the SRs are also become high around 105 to 106, but in areas where the frequencies of prenatal losses are relatively high then the SRs are found to be low around 102. Later on several researches have focused on temporal, regional and seasonal fluctuations of SR. In general, factors that affect the SR within the families remain poorly understood. Attempts to identify such factors in national birth registers are also remained to be unsuccessful. Recently, SR studies have mainly concentrated on the identification of general but occasional factors. In this study, we tried to identify the effects of issues like maternal age and type of delivery (live- and stillborn, singletons and multiples) to identify the controlling parameters of sex ratio during birth. Post experimental outcome showed that there is no significant difference between live- and stillborn and maternal age had as no significant effect for controlling sex ratio. The SR is higher among singletons than that of multiples, but there is no significant difference obtained in SR between twins and triplets. Among singletons the temporal differences are non-significant, but for twins and triplets, significant temporal differences were obtained.

##### A Comparison between Maximum Likelihood and Bayesian Estimation Methods for a Shape Parameter of the Weibull-Exponential Distribution

Terna G. Ieren, Pelumi E. Oguntunde

Asian Journal of Probability and Statistics, Page 1-12
DOI: 10.9734/ajpas/2018/v1i124504

We considered the Bayesian analysis of a shape parameter of the Weibull-Exponential distribution in this paper. We assumed a class of non-informative priors in deriving the corresponding posterior distributions. In particular, the Bayes estimators and associated risks were calculated under three different loss functions. The performance of the Bayes estimators was evaluated and compared to the method of maximum likelihood under a comprehensive simulation study. It was discovered that for the said parameters to be estimated, the quadratic loss function under both uniform and Jeffrey’s priors should be used for decreasing parameter values while the use of precautionary loss function can be preferred for increasing parameter values irrespective of the variations in sample size.