ASYMPTOTIC DISTRIBUTIONS FOR SUMS OF INDEPENDENT EXPONENTIALLY DISTRIBUTED RANDOM VARIABLES AND FOR THE PURE BIRTH PROCESS.Statistical distributionsRandom variablesExponential functionsStatistical processesSeriesConvergenceThe question of asymptotic distributions for the pure birth process is considered. For the ...
The amount of time a machine works before breaking down is exponentially distributed with mean 10. If the amount of time it takes a single repairman to fix a machine is exponentially distributed with mean 8, then (a) what is the average number of machines not in use? (b) what proportion...
The CLT is definitely the fundamental one in probability theory and statistics. Initially formulated for independent and identically distributed random variables, it was thereafter generalized to martingales (see [31]), which has constituted a background for proving various versions of the CLT pertaining...
which is linear in the idempotent algebra with operations of maximum and addition. It is assumed that some entries of the matrix are zero constants and all other entries are mutually independent and exponentially distributed. The problem considered is the computation of the Lyapunov exponent, which ...
To achieve these several objectives, we need to compute the probability distribution of the sum of independent and identically hypergeometric-distributed random variables. Show abstract The effect of measurement errors on the performance of the Exponentially Weighted Moving Average control charts for the ...
4. In the present study, an exponentially distributed model with the same acoustic power is modulated into a more realistic model. First, we introduce an exponentially distributed model in which two kinds of vehicles with different power levels are distributed independently on a road. The cumulant...
The estimate of the response variable becomes biased, does not converge to the true value, and its variance is larger than the true value. A pair of antithetic exponential random numbers is created by power transformation of uniformly distributed random [0,1] numbers. This pair of antithetic ...
In this paper the multiple linear regression model and three covariates were studied in the presence of the problem of auto-correlation of errors when the random error was distributed over the distribution of exponential. Three methods were compared (general least squar...
The combination of exponentially distributed quality characteristics with the MDS has been shown as an efficient monitoring technique for the mean of the production process [15]. Further literature on proposed approaches for quick detection of unusual changes can be consulted [16,17,18,19,20]. The...
2. Model and Notation Let {Xi, Yi}in=1 be n independent and identically distributed observations of random variables {X, Y} coming from an unknown distribution F(x, y), where Xi's are the dx- dimensional vector and Yi's are the dy-dimensional vector. It is assumed that Xi's are ...