Characterizations of the Exponentiated Marshall-Olkin Discrete Uniform Distribution

In this short paper, we consider certain characterizations of the Exponentiated Marshall-Olkin Discrete Uniform (EMODU) distribution introduced by Gharib et al. (2017) to complete in some manner, the authors'  work

Expectation Identity of the Discrete Uniform Distribution and Its Application in the Calculations of Higher-Order Origin Moments

We provide a novel method to analytically calculate the high-order origin moments of a Discrete Uniform (DU) random variable, that is, the expectation identity method. First, the expectation identity of the DU distribution is discovered and summarized in a theorem. After that, we analytically calculate the first four origin moments and the general kth (k=1,2,…) origin moment of the DU distribution by the expectation identity method. After comparing the corresponding coefficients on both sides of an equation, we obtain a nonhomogeneous linear equations of first degree in k+1 variables. Furthermore, we have provided two ways to solve the nonhomogeneous linear equations. The first way is by matrix inversion, and the second way is by iterative solving. Moreover, the coefficients of the first ten origin moments of the DU distribution are summarized in a table. Finally, we have a proposition for special summations.

Stochastic KEMIRA-M Approach with Consistent Weightings

This study proposes an advanced Modified KEmeny Median Indicator Rank Accordance (KEMIRA-M) approach based on stochastic evaluation process considering consistent weights to improve effective usage of KEMIRA-M. In the proposed approach, tasks related to the decision issue are performed by decision makers to ensure the understanding sufficiency of alternatives in terms of criteria more clearly. The weighting procedure of Analytic Hierarchy Process (AHP) is implemented in a stochastic manner benefited from discrete uniform distribution to provide obtaining consistent criteria weights considering median priority components. Therefore, different trials including different number of replications that shows the number of decision makers are performed and the most consistent weightings are determined for each trial in the stochastic process. In this way, the dependency to the limited numbers of decision makers and to determine criteria weights in a heuristic manner in KEMIRA-M is prevented. Additionally, the effect of the number of decision makers on criteria weightings and alternatives’ ranking process is shown. To obtain the most consistent weighting results, this stochastic process is utilized until acquiring approximate consistency ratios. The proposed stochastic KEMIRA-M approach is utilized to rank nine shopping malls (SMs) in Ankara in terms of technical criteria (TC) and universal design criteria (UDC). It was seen from the ranking results that the first SM (SM1) is the best one.

Probability Functions of Order Statistics from Discrete Uniform Distribution

In this paper, we firstly give basic definitions and theorems for order statistics. Later, we show that r. probability function of order statistics from discrete uniform distribution can be obtained in another form.

THE APPLICATION OF BENFORD'S LAW IN PSYCHOLOGICAL PRICING DETECTION

This paper presents the application of Benford's law in psychological pricing detection. Benford's law is naturally occurring law which states that digits have predictable frequencies of appearance with digit one having the highest frequency. Psychological pricing is one of the marketing pricing strategies directed on price setting which have the psychological impact on certain consumers. In order to investigate the application of Benford's law in psychological pricing detection, Benford's law is observed in the case of first and last digits. In order to inspect if the first and last digits of the observed prices are distributed according to the Benford’s law distribution or discrete uniform distribution respectively, mean absolute deviation measure, chi-square tests and Kolmogorov-Smirnov Z tests are used. Results of the analysis conducted on three price datasets have shown that the most dominating first digits are 1 and 2. On the other side, the most dominating last digits are 0, 5 and 9 respectively. The chi-square tests and Kolmogorov-Smirnov Z tests have showed that, at significance level of 5%, none of the three observed price datasets does have first digit distribution that fits to the Benford’s law distribution. Likewise, mean absolute deviation values have shown that there are large differences between the last digit distributions and the discrete uniform distribution implying psychological pricing in all price datasets.

Moments of sample extremes of order statistics from discrete uniform distribution and numerical results

In this study, the mth raw moments of sample extremes of order statistics from discrete uniform distribution are obtained. The results of sample extremes of order statistics of random variable for the independent and identically discrete uniform distribution are given. Numerical values are shown in table form

استعمال خوارزمية سرب الطيور لحل نماذج صفوف الانتظار مع تطبيق عملي

المستخلص يتضمن هذا البحث تطبيق نظرية صفوف الانتظار مع خوارزمية سرب الطيور أو ما يسمى ب(ذكاء السرب) لحل مشكلة صفوف الانتظار وتطويرها للهيئة العامة للضرائب / فرع كرخ المركز في مرحلة الخدمة لقسم الحاسبة المتآلف من ستة موظفين, وتم أختيار نموذج صف الانتظار ذو قناة الخدمة الواحدة M/M/1 بحسب طبيعة عمل الدائرة المذكورة أنفاً ويكون مقسم حسب نظام الأحرف لكل موظف, وتم جمع البيانات المتآلفة من الأوقات ( وقت الوصول, وقت الخدمة, وقت المغادرة ) بالدقائق, حيث تم اختبار البيانات المستحصل عليها ووجد أنها تتوزع التوزيع الأحصائي الذي يتنــاسب مع طبيـــعة البيانات وعند أختبـارها وجــد أنها تتوزع توزيع الوصـــــول ( التوزيع المنتظم المتقطع Discrete Uniform distribution ) وتوزيع الخـدمة (التوزيع الآسي Exponential distribution ), وإيجاد مقاييس ألاداء ( الخدمة المقدمة) في النظام Ls , Lq , Ws , Wq) ), و تم حل مشكلة البحث بأستخدام برنامج MATLAB R2013a Version : 8.1 والحصول على النتائج المطلوبة, ويهدف البحث لحل مشكلة صفوف الانتظار لهيئة العامة للضرائب / فرع كرخ المركز وتقليل من أوقات الانتظار الزبائن وتحسين كفاءة الخدمة المقدمة.