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InverseCDF

InverseCDF
gives the inverse of the cumulative distribution function for the symbolic distribution dist as a function of the variable q.
  • The inverse CDF at q is also referred to as the q^(th) quantile of a distribution.
  • For a continuous distribution dist the inverse CDF at q is the value x such that CDF[dist, x]=q.
  • For a discrete distribution dist the inverse CDF at q is the smallest integer x such that CDF[dist, x]≥q.
  • The value q can be symbolic or any number between 0 and 1.
The inverse CDF for a continuous univariate distribution:
The inverse CDF for a discrete univariate distribution:
The inverse CDF for a continuous univariate distribution:
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The inverse CDF for a discrete univariate distribution:
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Obtain exact numeric results:
Obtain a machine-precision result:
Obtain a result at any precision for continuous distributions:
Obtain an exact result at any precision q for discrete distributions:
Plot the inverse CDF for a standard normal distribution:
Plot the inverse CDF for a binomial distribution:
Generate a random number from a distribution:
InverseCDF and CDF are inverses for continuous distributions:
Compositions of InverseCDF and CDF give step functions for a discrete distribution:
InverseCDF is equivalent to Quantile for distributions:
Symbolic closed forms do not exist for some distributions:
Numerical evaluation works:
Substitution of invalid values into symbolic outputs gives results that are not meaningful:
When giving the input as argument complete checking is done:
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