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For k ≤ np, upper bounds can be derived for the lower tail of the cumulative distribution function (;,) = (), the probability that there are at most k successes. Since Pr ( X ≥ k ) = F ( n − k ; n , 1 − p ) {\displaystyle \Pr(X\geq k)=F(n-k;n,1-p)} , these bounds can also be seen as bounds for the upper tail of the cumulative ...
Cumulative distribution function for the exponential distribution Cumulative distribution function for the normal distribution. In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable, or just distribution function of , evaluated at , is the probability that will take a value less than or equal to .
The multinomial distribution, a generalization of the binomial distribution. The multivariate normal distribution, a generalization of the normal distribution. The multivariate t-distribution, a generalization of the Student's t-distribution. The negative multinomial distribution, a generalization of the negative binomial distribution.
In statistics, cumulative distribution function (CDF)-based nonparametric confidence intervals are a general class of confidence intervals around statistical functionals of a distribution. To calculate these confidence intervals, all that is required is an independently and identically distributed (iid) sample from the distribution and known ...
The function g is the cumulative distribution function (cdf) of some probability distribution. Usually this probability distribution has a support from minus infinity to plus infinity so that any finite value of η is transformed by the function g to a value inside the range 0 to 1.
Different texts (and even different parts of this article) adopt slightly different definitions for the negative binomial distribution. They can be distinguished by whether the support starts at k = 0 or at k = r, whether p denotes the probability of a success or of a failure, and whether r represents success or failure, [1] so identifying the specific parametrization used is crucial in any ...
The Wilson score interval [12] provides confidence interval for binomial distributions based on score tests and has better sample coverage, see [13] and binomial proportion confidence interval for a more detailed overview. Instead of the "Wilson score interval" the "Wald interval" can also be used provided the above weight factors are included.
The beta-binomial distribution is the binomial distribution in which the probability of success at each of n trials is not fixed but randomly drawn from a beta distribution. It is frequently used in Bayesian statistics , empirical Bayes methods and classical statistics to capture overdispersion in binomial type distributed data.