In this paper, a new probability distribution is proposed by using Marshall and Olkin transformation. Some of its properties such as moments, moment generating function, order statistics and reliability functions are ...In this paper, a new probability distribution is proposed by using Marshall and Olkin transformation. Some of its properties such as moments, moment generating function, order statistics and reliability functions are derived. The method of </span><span style="font-family:Verdana;">maximum likelihood is used to estimate the model parameters. The graphs of the reliability function and hazard rate function are plotted by taken some values of the parameters. Three real life applications are introduced to compare the behaviour of the new distribution with other distributions.展开更多
In this paper, we study a new version from Dual-pivot Quicksort algorithm when we have some other number of pivots. Hence, we discuss the idea of picking pivots ?by random way and splitting the list simultaneously acc...In this paper, we study a new version from Dual-pivot Quicksort algorithm when we have some other number of pivots. Hence, we discuss the idea of picking pivots ?by random way and splitting the list simultaneously according to these. The modified version generalizes these results for multi process. We show that the average number of swaps done by Multi-pivot Quicksort process and we present a special case. Moreover, we obtain a relationship between the average number of swaps of Multi-pivot Quicksort and Stirling numbers of the first kind.展开更多
Sorting an array of objects such as integers, bytes, floats, etc is considered as one of the most important problems in Computer Science. Quicksort is an effective and wide studied sorting algorithm to sort an array o...Sorting an array of objects such as integers, bytes, floats, etc is considered as one of the most important problems in Computer Science. Quicksort is an effective and wide studied sorting algorithm to sort an array of n distinct elements using a single pivot. Recently, a modified version of the classical Quicksort was chosen as standard sorting algorithm for Oracles Java 7 routine library due to Vladimir Yaroslavskiy. The purpose of this paper is to present the different behavior of the classical Quicksort and the Dual-pivot Quicksort in complexity. In Particular, we discuss the convergence of the Dual-pivot Quicksort process by using the contraction method. Moreover we show the distribution of the number of comparison done by the duality process converges to a unique fixed point.展开更多
文摘In this paper, a new probability distribution is proposed by using Marshall and Olkin transformation. Some of its properties such as moments, moment generating function, order statistics and reliability functions are derived. The method of </span><span style="font-family:Verdana;">maximum likelihood is used to estimate the model parameters. The graphs of the reliability function and hazard rate function are plotted by taken some values of the parameters. Three real life applications are introduced to compare the behaviour of the new distribution with other distributions.
文摘In this paper, we study a new version from Dual-pivot Quicksort algorithm when we have some other number of pivots. Hence, we discuss the idea of picking pivots ?by random way and splitting the list simultaneously according to these. The modified version generalizes these results for multi process. We show that the average number of swaps done by Multi-pivot Quicksort process and we present a special case. Moreover, we obtain a relationship between the average number of swaps of Multi-pivot Quicksort and Stirling numbers of the first kind.
文摘Sorting an array of objects such as integers, bytes, floats, etc is considered as one of the most important problems in Computer Science. Quicksort is an effective and wide studied sorting algorithm to sort an array of n distinct elements using a single pivot. Recently, a modified version of the classical Quicksort was chosen as standard sorting algorithm for Oracles Java 7 routine library due to Vladimir Yaroslavskiy. The purpose of this paper is to present the different behavior of the classical Quicksort and the Dual-pivot Quicksort in complexity. In Particular, we discuss the convergence of the Dual-pivot Quicksort process by using the contraction method. Moreover we show the distribution of the number of comparison done by the duality process converges to a unique fixed point.
