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Problem statement: The distributions of R = X+Y and W = X/(X+Y), where X and Y follow Lawrance and Lewis`s bivariate exponential distribution, is generalized. Approach: In this research we found mixtures of sum of bivariate exponential random variables. Results: Also we calculated the probability density function (pdf) of the random sum of mixtures of sum of bivariate exponential random variables. Conclusion/Recommendations: In this study we investigated the pdf of random sum of mixtures of sum of bivariate exponential random variables

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In this paper, we study the estimation of the spectral density function and properties of the resulting estimator which called the periodogram. The statistical properties for this periodogram in case of actual observations and forecasted observations of the fuzzy time series are studied. Depending on MSEs which based on these statistical properties, the periodogram results can be compared in both cases. For this purpose a program that transfer the observed time series to fuzzy time series with large sizes is constructed.

This paper considers a new model in search theory to find a randomly located target in the 3-dimensional space. An approximation algorithm that facilitates searching procedures for searchers or robots is presented. The expected time to detect the target is also proved. The statistical analysis by calculating the optimal search strategy which minimizes the time to detect the target, assuming trivariate standard normal distribution is provided, and the technique by flowcharts is designed as well. The effectiveness of this strategy is illustrated by introducing an application from real world.