Search results
Results from the WOW.Com Content Network
2.1 Low-order polylogarithms. 2.2 Exponential function. ... 7.2 Sum of reciprocal of factorials. 7.3 Trigonometry and ...
In the shape-scale parametrization, X ~ Gamma(1, λ) has an exponential distribution with rate parameter 1/λ. If X ~ Gamma(ν/2, 2) (in the shape–scale parametrization), then X is identical to χ 2 (ν), the chi-squared distribution with ν degrees of freedom. Conversely, if Q ~ χ 2 (ν) and c is a positive constant, then cQ ~ Gamma(ν/2 ...
Examples: [3] [4] If X 1 and X 2 are Poisson random variables with means μ 1 and μ 2 respectively, then X 1 + X 2 is a Poisson random variable with mean μ 1 + μ 2. The sum of gamma (α i, β) random variables has a gamma (Σα i, β) distribution.
The sum of exponentials is a useful model in pharmacokinetics (chemical kinetics in general) for describing the concentration of a substance over time. The exponential terms correspond to first-order reactions, which in pharmacology corresponds to the number of modelled diffusion compartments. [2] [3]
An exact 100(1 − α)% confidence interval for the rate parameter of an exponential distribution is given by: [13] ^, < < ^,, which is also equal to ¯, < < ¯,, where χ 2 p , v is the 100( p ) percentile of the chi squared distribution with v degrees of freedom , n is the number of observations and x-bar is the sample average.
In probability theory, an exponentially modified Gaussian distribution (EMG, also known as exGaussian distribution) describes the sum of independent normal and exponential random variables. An exGaussian random variable Z may be expressed as Z = X + Y, where X and Y are independent, X is Gaussian with mean μ and variance σ 2, and Y is ...
The distribution of the product of a random variable having a uniform distribution on (0,1) with a random variable having a gamma distribution with shape parameter equal to 2, is an exponential distribution. [18]
The Erlang distribution is the distribution of a sum of independent exponential variables with mean / each. Equivalently, it is the distribution of the time until the kth event of a Poisson process with a rate of . The Erlang and Poisson distributions are complementary, in that while the Poisson distribution counts the events that occur in a ...