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The median of a normal distribution with mean μ and variance σ 2 is μ. In fact, for a normal distribution, mean = median = mode. The median of a uniform distribution in the interval [a, b] is (a + b) / 2, which is also the mean. The median of a Cauchy distribution with location parameter x 0 and scale parameter y is x 0, the location parameter.
A median m cannot lie too far ... The binomial distribution converges towards the Poisson distribution as the number of trials goes to infinity while the product np ...
As k goes to infinity, the Weibull distribution converges to a Dirac delta distribution centered at x = λ. Moreover, the skewness and coefficient of variation depend only on the shape parameter. A generalization of the Weibull distribution is the hyperbolastic distribution of type III.
The law of large numbers as well as the central limit theorem are partial solutions to a general problem: "What is the limiting behavior of S n as n approaches infinity?" In mathematical analysis, asymptotic series are one of the most popular tools employed to approach such questions.
then as tends to infinity, converges in probability (see below) to the common mean, , of the random variables . This result is known as the weak law of large numbers . Other forms of convergence are important in other useful theorems, including the central limit theorem .
The median is the value such that the fractions not exceeding it and not falling below it are each at least 1/2. It is not necessarily unique, but never infinite or totally undefined. For a data sample it is the "halfway" value when the list of values is ordered in increasing value, where usually for a list of even length the numerical average ...
People often think the MAPE will be optimized at the median. But for example, a log normal has a median of e μ {\displaystyle e^{\mu }} where as its MAPE is optimized at e μ − σ 2 {\displaystyle e^{\mu -\sigma ^{2}}} .
Then as approaches infinity, the random variables () converge in distribution to a normal (,): [1] The central limit theorem gives only an asymptotic distribution. As an approximation for a finite number of observations, it provides a reasonable approximation only when close to the peak of the normal distribution; it requires a very large ...