Computing the Joint Distribution of General Linear Combinations of Spacings or Exponential Variates
نویسنده
چکیده
We present an algorithm for computing exact expressions for the distribution of the maximum or minimum of an arbitrary nite collection of linear combinations of spacings or exponential random variables with rational coeecients. These expressions can then be manipulated or evaluated using symbolic math packages such as MAPLE. As examples, we apply this algorithm to obtain the distributions of the maximum and minimum of a moving average process, and the distribution of the Kolmogorov-Smirnov statistic.
منابع مشابه
Sequential estimation of linear combinations of the location and scale parameters in negative exponential distribution
Sequential estimation is used where the total sample size is not fix and the problem cannot solve with this fixed sample size. Sequentially estimating the mean in an exponential distribution (one and two parameter), is an important problem which has attracted attentions from authors over the years. These largely addressed an exponential distribution involving a single or two parameters. In t...
متن کاملBivariate Exponential Distributions Using Linear Structures
We derive bivariate exponential distributions using independent auxiliary random variables. We develop separate models for positive and negative correlations between the exponentially distributed variates. To obtain a positive correlation, we define a linear relation between the variates X and Y of the form Y = aX +Z where a is a positive constant and Z is independent of X. To obtain exponentia...
متن کاملLongest Path in Networks of Queues in the Steady-State
Due to the importance of longest path analysis in networks of queues, we develop an analytical method for computing the steady-state distribution function of longest path in acyclic networks of queues. We assume the network consists of a number of queuing systems and each one has either one or infinite servers. The distribution function of service time is assumed to be exponential or Erlang. Fu...
متن کاملON THE SZEGED INDEX OF NON-COMMUTATIVE GRAPH OF GENERAL LINEAR GROUP
Let $G$ be a non-abelian group and let $Z(G)$ be the center of $G$. Associate with $G$ there is agraph $Gamma_G$ as follows: Take $Gsetminus Z(G)$ as vertices of$Gamma_G$ and joint two distinct vertices $x$ and $y$ whenever$yxneq yx$. $Gamma_G$ is called the non-commuting graph of $G$. In recent years many interesting works have been done in non-commutative graph of groups. Computing the clique...
متن کاملEffects of statistical distribution of joint trace length on the stability of tunnel excavated in jointed rock mass
The rock masses in a construction site of underground cavern are generally not continuous, due to the presence of discontinuities, such as bedding, joints, faults, and fractures. The performance of an underground cavern is principally ruled by the mechanical behaviors of the discontinuities in the vicinity of the cavern. During underground excavation, many surrounding rock failures have close r...
متن کامل