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In probability and statistics, the quantile function outputs the value of a random variable such that its probability is less than or equal to an input probability value. Intuitively, the quantile function associates with a range at and below a probability input the likelihood that a random variable is realized in that range for some ...
The area below the red curve is the same in the intervals (−∞,Q 1), (Q 1,Q 2), (Q 2,Q 3), and (Q 3,+∞). In statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, or dividing the observations in a sample in the same way. There is one fewer ...
In statistics, a Q–Q plot (quantile–quantile plot) is a probability plot, a graphical method for comparing two probability distributions by plotting their quantiles against each other. [1] A point ( x , y ) on the plot corresponds to one of the quantiles of the second distribution ( y -coordinate) plotted against the same quantile of the ...
Boxplot (with an interquartile range) and a probability density function (pdf) of a Normal N(0,σ 2) Population. In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. [1]
Since it is based on quantile information, it is less sensitive to outliers than measures such as the coefficient of variation. As such, it is one of several robust measures of scale . The statistic is easily computed using the first and third quartiles , Q 1 and Q 3 , respectively) for each data set.
In particular, the quantile is 1.96; therefore a normal random variable will lie outside the interval in only 5% of cases. The following table gives the quantile z p {\textstyle z_{p}} such that X {\textstyle X} will lie in the range μ ± z p σ {\textstyle \mu \pm z_{p}\sigma } with a specified probability p {\textstyle p} .
A quantile-based credible interval, which is computed by taking the inter-quantile interval [, +] for some predefined [,]. For instance, the median credible interval (MCI) of probability γ {\displaystyle \gamma } is the interval where the probability of being below the interval is as likely as being above it, that is to say the interval [ q ...
The cumulants of the uniform distribution on the interval [−1, 0] are κ n = B n /n, where B n is the n th Bernoulli number. The cumulants of the exponential distribution with rate parameter λ are κ n = λ −n (n − 1)!.