In this paper, we considered the half logistic model and derived a probability density function that generalized it. The cumulative distribution function, the $n^{th}$ moment, the median, the mode and the 100$k$-percentage points of the generalized distribution were established. Estimation of the parameters of the distribution through maximum likelihood method was accomplished with the aid of c...

Based on recent studies by Guy Jumarie [1] which defines probability density of fractional order and fractional moments by using fractional calculus (fractional derivatives and fractional integration), this study expands the concept of probability density of fractional order by defining the fractional probability measure, which leads to a fractional probability theory parallel to the classical ...

In the present investigation transient, G x/G/m queuing model with balking and reneging has been studied. The diffusion process with elementary return boundary has been used for modeling purpose. The probability density function (p. d. f.) for the number of customers in the system has been obtained. In special case, the steady state results that tally with those of Kimura and Ohsone have been e...

Based on probability density evolution method (PDEM) and Bayes’ law, a new filter strategy is proposed, in which the prior of system state interest predicted by solving generalized equation (GDEE), posterior then updated terms Bayesian formula. Furthermore, Chebyshev polynomial-based collocation developed to obtain numerical solutions probability. Three illustrative examples are finally present...

In this study, we considered an inflationary inventory control model under non-deterministic conditions. We assumed the inflation rate as a normal distribution, with any arbitrary probability density function (pdf). The objective function was to minimize the total discount cost of the inventory system. We used two methods to solve this problem. One was the classic numerical approach which turne...

In this study, the difference between the mean of the Rayleigh Probability Density Function and the mean obtained from the graph of Rayleigh Probability Density Function is minimized by changing the coefficient in the equation yielding the mean. By using various numbers of data and K values, Rayleigh Probability Density Function is plotted with the means mentioned above.