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... To obtain a partial generalization of Theorem II of Horadam and the corresponding proposition of 5ubbaRao,we first define {U^} * a fundamental sequence of order r; we illustrate its fundamental nature by showing that any linear recursive sequence of order v can be expressed in terms of {U^}. We defi ...
... To obtain a partial generalization of Theorem II of Horadam and the corresponding proposition of 5ubbaRao,we first define {U^} * a fundamental sequence of order r; we illustrate its fundamental nature by showing that any linear recursive sequence of order v can be expressed in terms of {U^}. We defi ...
Power Normal Distribution - IITK - Indian Institute of Technology
... Lindley-Singpurwalla distribution, see [23]. Multivariate generalization and the generalization for the other distribution functions are also possible along the same line. It can be easily seen that the bivariate power normal distribution is an absolute continuous distribution. The joint probabilit ...
... Lindley-Singpurwalla distribution, see [23]. Multivariate generalization and the generalization for the other distribution functions are also possible along the same line. It can be easily seen that the bivariate power normal distribution is an absolute continuous distribution. The joint probabilit ...
On independent sets in purely atomic probability spaces with
... Ghosh [6] show that the number of nontrivial independent events in such spaces cannot be more than Ω(m) where m is the cardinality of the space. This result should be seen in view of the known fact (see [7, Problem 50, Section 4.1]) that if A1 , A2 , . . . , An are independent non-trivial events of ...
... Ghosh [6] show that the number of nontrivial independent events in such spaces cannot be more than Ω(m) where m is the cardinality of the space. This result should be seen in view of the known fact (see [7, Problem 50, Section 4.1]) that if A1 , A2 , . . . , An are independent non-trivial events of ...
(pdf)
... If X is a random variable, then for every Borel subset B of R, X −1 (B) ∈ F. We define a measure µX , called the distribution of the random variable, on Borel sets by µX (B) := P{X ∈ B} = {X −1 (B)}. If µX takes values only for countable subsets of the real numbers, X is a discrete random variable; ...
... If X is a random variable, then for every Borel subset B of R, X −1 (B) ∈ F. We define a measure µX , called the distribution of the random variable, on Borel sets by µX (B) := P{X ∈ B} = {X −1 (B)}. If µX takes values only for countable subsets of the real numbers, X is a discrete random variable; ...
sec7.2
... When we want information about the population proportion p of successes, we ˆ to estimate the unknown often take an SRS and use the sample proportion p parameter p. The sampling distribution of pˆ describes how the statistic varies in all possible samples from the population. ...
... When we want information about the population proportion p of successes, we ˆ to estimate the unknown often take an SRS and use the sample proportion p parameter p. The sampling distribution of pˆ describes how the statistic varies in all possible samples from the population. ...
Central limit theorem
In probability theory, the central limit theorem (CLT) states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined expected value and well-defined variance, will be approximately normally distributed, regardless of the underlying distribution. That is, suppose that a sample is obtained containing a large number of observations, each observation being randomly generated in a way that does not depend on the values of the other observations, and that the arithmetic average of the observed values is computed. If this procedure is performed many times, the central limit theorem says that the computed values of the average will be distributed according to the normal distribution (commonly known as a ""bell curve"").The central limit theorem has a number of variants. In its common form, the random variables must be identically distributed. In variants, convergence of the mean to the normal distribution also occurs for non-identical distributions or for non-independent observations, given that they comply with certain conditions.In more general probability theory, a central limit theorem is any of a set of weak-convergence theorems. They all express the fact that a sum of many independent and identically distributed (i.i.d.) random variables, or alternatively, random variables with specific types of dependence, will tend to be distributed according to one of a small set of attractor distributions. When the variance of the i.i.d. variables is finite, the attractor distribution is the normal distribution. In contrast, the sum of a number of i.i.d. random variables with power law tail distributions decreasing as |x|−α−1 where 0 < α < 2 (and therefore having infinite variance) will tend to an alpha-stable distribution with stability parameter (or index of stability) of α as the number of variables grows.