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Questions tagged [quantile]

one of several equally-frequent subranges of a data set or random distribution; for example, a percentile or quartile

A set of quantiles is a partition of the range of a random variable or set of data into subranges of equal likelihood or frequency (or approximately equal likelihood or frequency if an equal partition is not possible). An $n$-quantile is one of a set of quantiles that partition the range into $n$ such parts.

Common examples of quantiles are quartiles ($4$-quantiles), quintiles ($5$-quantiles), deciles ($10$-quantiles), percentiles ($100$-quantiles), and the median (a $2$-quantile).

138 questions
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How do you differentiate the unconditional quantile function for y wrt to P(x=1) where x is a Bernoulli random variable?

Suppose $X$ is a Bernoulli random variable (0,1). The marginal cdf of $Y$ can be written. $F_Y(y)$ = $Pr(X=1)*F_{Y|X=1}(y)$ + $Pr(X=0)*F_{Y|X=0}(y)$ (Eq. 1) Replace $y$ with $q_Y(\tau;p)$, the quantile function for $y$, indexed by $p=Pr(X=1)$ We…
SWF
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How to resolve ties in quantile distribution

What rules are available for deciding which quantile a particular value would fall into when the boundaries of more than one quantile are identical? My data set includes score ranging between 1 and 20. As there are a lot of scores of 15, my…
charliefortune
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Quantile function question

is there a way how to get quantile function from random variable $Y$ defined as: $$ Y = \begin{cases} 0 \text{ ... with probability 0.25}\\ f(x) \text{ ... with probability 0.75} \end{cases} $$ where…
Andrej H.
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CDF and Quantile Function

Assume that $F_X$ is the CDF of the random variable X and $Q_X$ its quantile function.Prove that $Q_X(F_X(t)) \le t $ and $F_X(Q_X(p)) \ge p $. I substituted $F_X(t)=P[X \le t]$ and then substituted that in the quantile function…
Raveesh
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