
In general, the Quantile Functions (sometimes referred to
as Inverse Density Functions or Percent Point Functions) return the
Value X at which P(X) = [specified cumulative probability], given that particular
distribution.
 IDF_Beta: This
function takes the specified probability and returns the value X, such
that P(X) = Pvalue, given the Beta distribution with the two
specified Shape parameters. Because the formula for this function does
not exist in a closed form, it must be computed numerically. This
script arrives at the Xvalue through an iterative process, repeatedly
testing Xvalues with the CDF_Beta function until it arrives at P
value that is within 1x10^{12} units from the specified
Pvalue (this usually takes between 3060 iterations).
a) Parameters:
 Pvalue: Number (0 >= p
>= 1)
 Shape1: Number > 0
 Shape2: Number > 0
b) Usages:
 From "Probability Distribution Calculator",
select "Quantile (IDF)" and Beta distribution.
 (Avenue): theProb = av.Run("Jennessent.DistFunc”,
{“IDF_Beta”, {Pvalue, Shape1, Shape2}})
 (Avenue): theProb =
av.Run("Jennessent.TableDistFunc”, {“IDF_Beta”, {Pvalue, Shape1,
Shape2}})
 (Avenue): theProb = av.Run("Jennessent.IDF_Beta",
{Pvalue, Shape1, Shape2})
c) Function: 

 IDF_Binomial:
This function takes the specified probability and returns the value X
such that the Probability of getting (X – 1) successes <= the Specified
Probability. This function takes an iterative approach to finding the
correct X value, repeatedly trying different values of X until it
reaches the correct one. This iterative process rarely takes more than
25 repetitions.
a) Parameters:
 Pvalue: Number (0 >= p >= 1)
 # Trials: Integer >= 2, # Successes
 Probability of Success: Number (0 >= p >= 1)
b) Usages:
 From "Probability Distribution Calculator", select
"Quantile (IDF)" and Binomial distribution.
 (Avenue): theProb = av.Run("Jennessent.DistFunc”,
{“IDF_Binomial”, {Pvalue, #Trials, Probability of Success}})
 (Avenue): theProb =
av.Run("Jennessent.TableDistFunc”, {“IDF_Binomial”, {Pvalue, #Trials,
Probability of Success}})
 (Avenue): theProb =
av.Run("Jennessent.IDF_Binomial", {Pvalue, #Trials, Probability of
Success})
c) Function: 

 IDF_Cauchy:
This function takes the specified probability and returns the value X,
such that P(X) = Pvalue, given the Cauchy distribution with the
specified location and scale parameters. The Standardized Cauchy
distribution has Location = 0 and Scale = 1.
a)
Parameters:
 Pvalue: Number (0 >= p >= 1)
 Location: Number
 Scale: Number > 0
b) Usages:
 From "Probability Distribution Calculator", select
"Quantile (IDF)" and Cauchy distribution.
 (Avenue): theProb = av.Run("Jennessent.DistFunc”,
{“IDF_Cauchy”, {Pvalue, Location, Scale}})
 (Avenue): theProb =
av.Run("Jennessent.TableDistFunc”, {“IDF_Cauchy”, {Pvalue, Location,
Scale}})
 (Avenue): theProb = av.Run("Jennessent.IDF_Cauchy",
{Pvalue, Location, Scale})
c) Function: 

 IDF_ChiSquare:
This function takes the specified probability and returns the value X,
such that P(X) = Pvalue, given the ChiSquare distribution with the
specified Degrees of Freedom. Because the formula for this function does
not exist in a closed form, it must be computed numerically. This script
arrives at the Xvalue through an iterative process, repeatedly testing
Xvalues with the CDF_ChiSquare function until it arrives at P value
that is within 1x10 12 units from the specified Pvalue (this usually
takes between 3060 iterations). The ChiSquare distribution results
when v (where v = Degrees of Freedom) independent variables with
standard normal distributions are squared and summed (Croarkin & Tobias,
Date unknown).
a) Parameters:
 Pvalue: Number (0 >= p >= 1)
 Degrees of Freedom: Number > 0
b) Usages:
 From "Probability Distribution Calculator", select
"Quantile (IDF)" and Chi Square distribution.
 (Avenue): theProb = av.Run("Jennessent.DistFunc”,
{“IDF_ChiSquare”, {Pvalue, DF}})
 (Avenue): theProb =
av.Run("Jennessent.TableDistFunc”, {“IDF_ChiSquare”, {Pvalue, DF}})
 (Avenue): theProb =
av.Run("Jennessent.IDF_ChiSquare", {Pvalue, DF})
c) Function: 

 IDF_Exp: This
function takes the specified probability and returns the value X, such
that P(X) = Pvalue, given the Exponential distribution with the
specified mean. This script uses the 1parameter version of the equation
(i.e. assuming Location = 0). The Standard Exponential Distribution is
that which has Mean = 1.
a) Parameters:
 Pvalue: Number (0 >= p >= 1)
 Mean: Number > 0
b) Usages:
 From "Probability Distribution Calculator", select
"Quantile (IDF)" and Exponential distribution.
 (Avenue): theProb = av.Run("Jennessent.DistFunc”,
{“IDF_Exp”, {Pvalue, Mean}})
 (Avenue): theProb =
av.Run("Jennessent.TableDistFunc”, {“IDF_Exp”, {Pvalue, Mean}})
 (Avenue): theProb = av.Run("Jennessent.IDF_Exp",
{Pvalue, Mean})
c) Function: 

 IDF_F: This function
takes the specified probability and returns the value X, such that P(X)
= Pvalue, given the F distribution with the specified Degrees of
Freedom. Because the formula for this function does not exist in a
closed form, it must be computed numerically. This script arrives at the
Xvalue through an iterative process, repeatedly testing Xvalues with
the CDF_F function until it arrives at P value that is within 1x10^{12}
units from the specified Pvalue (this usually takes between 3060
iterations). The F distribution is the ratio of two Chi Square
distributions with ratios v_{1} and v_{2} respectively.
a) Parameters:
 Pvalue: Number (0 >= p >= 1)
 1st Degrees of Freedom: Number > 1
 2nd Degrees of Freedom: Number > 1
b) Usages:
 From "Probability Distribution Calculator", select
"Quantile (IDF)" and F distribution.
 (Avenue): theProb = av.Run("Jennessent.DistFunc”,
{“IDF_F”, {Pvalue, DF1, DF2}})
 (Avenue): theProb =
av.Run("Jennessent.TableDistFunc”, {“IDF_F”, {Pvalue, DF1, DF2}})
 (Avenue): theProb = av.Run("Jennessent.IDF_F",
{Pvalue, DF1, DF2})
c) Function: 

 IDF_Logistic:
This function takes the specified probability and returns the value X,
such that P(X) = Pvalue, given the Logistic distribution with the
specified mean and scale parameters.
a)
Parameters:
 Pvalue: Number (0 >= p >= 1)
 Mean: Number
 Scale: Number > 0
b) Usages:
 From "Probability Distribution Calculator", select
"Quantile (IDF)" and Logistic distribution.
 (Avenue): theProb = av.Run("Jennessent.DistFunc”,
{“IDF_Logistic”, {Pvalue, Mean, Scale}})
 (Avenue): theProb =
av.Run("Jennessent.TableDistFunc”, {“IDF_Logistic”, {Pvalue, Mean,
Scale}})
 (Avenue): theProb =
av.Run("Jennessent.IDF_Logistic", {Pvalue, Mean, Scale})
c) Function: 

 IDF_LogNormal:
This function takes the specified probability and returns the value X,
such that P(X) = Pvalue, given the LogNormal distribution with the
specified mean and scale parameters. Because the formula for this
function does not exist in a closed form, it must be computed
numerically. This script arrives at the Xvalue through an iterative
process, repeatedly testing Xvalues with the CDF_LogNormal function
until it arrives at P value that is within 1x10^{12} units from
the specified Pvalue (this usually takes between 3060 iterations). A
LogNormal distribution occurs when natural logarithms of variable X are
normally distributed. The Standard LogNormal Distribution is that with
Mean = 0 and Scale = 1. The 2Parameter LogNormal Distribution is that
with Mean = 0.
a) Parameters:
 Pvalue: Number (0 >= p >= 1)
 Mean: Number > 0
 Scale: Number > 0
b) Usages:
 From "Probability Distribution Calculator", select
"Quantile (IDF)" and LogNormal distribution.
 (Avenue): theProb = av.Run("Jennessent.DistFunc”,
{“IDF_LogNormal, {Pvalue, Mean, Scale}})
 (Avenue): theProb =
av.Run("Jennessent.TableDistFunc”, {“IDF_LogNormal, {Pvalue, Mean,
Scale}})
 (Avenue): theProb =
av.Run("Jennessent.IDF_LogNormal", {Pvalue, Mean, Scale})
c) Function: 

 IDF_Normal:
This function takes the specified probability and returns the value X,
such that P(X) = Pvalue, given the Normal distribution with the
specified mean and standard deviation. Because the formula for this
function does not exist in a closed form, it must be computed
numerically. This script arrives at the Xvalue through an iterative
process, repeatedly testing Xvalues with the CDF_Normal_Simpsons
function until it arrives at P value that is within 1x10^{12}
units from the specified Pvalue (this usually takes between 3060
iterations). Furthermore, there is no closed formula for calculating the
Normal cumulative distribution function, so this script uses the
Simpson’s approximation method (Stewart 1998, p. 421424) to calculate a
highly accurate estimate (accuracy to > 12 decimal places). The Standard
Normal Distribution is that with Mean = 0 and Standard Deviation = 1.
a) Parameters:
 Pvalue: Number (0 >= p >= 1)
 Mean: Number
 Standard Deviation: Number > 0
b) Usages:
 From "Probability Distribution Calculator", select
"Quantile (IDF)" and Normal distribution.
 (Avenue): theProb = av.Run("Jennessent.DistFunc”,
{“IDF_Normal_Simpsons, {Pvalue, Mean, St. Dev.}})
 (Avenue): theProb =
av.Run("Jennessent.TableDistFunc”, {“IDF_Normal_Simpsons, {Pvalue,
Mean, St. Dev.}})
 (Avenue): theProb =
av.Run("Jennessent.IDF_Normal_Simpsons", {Pvalue, Mean, St. Dev.})
c) Function: 

 IDF_Poisson: This
function takes the specified probability and returns the value X such
that the Probability of getting (X – 1) events <= the Specified
Probability. This function takes an iterative approach to finding the
correct X value, repeatedly trying different values of X until it
reaches the correct one.
a) Parameters:
 Pvalue: Number (0 >= p >= 1)
 Mean: Number > 0
b) Usages:
 From "Probability Distribution Calculator", select
"Quantile (IDF)" and Poisson distribution.
 (Avenue): theProb = av.Run("Jennessent.DistFunc”,
{“IDF_Poisson, {#Pvalue, Mean}})
 (Avenue): theProb =
av.Run("Jennessent.TableDistFunc”, {“IDF_Poisson, {Pvalue, Mean}})
 (Avenue): theProb =
av.Run("Jennessent.IDF_Poisson", {Pvalue, Mean})
c) Function: 

 IDF_StudentsT:
This function takes the specified probability and returns the value X,
such that P(X) = Pvalue, given the Student’s T distribution with the
specified Degrees of Freedom. Because the formula for this function does
not exist in a closed form, it must be computed numerically. This script
arrives at the Xvalue through an iterative process, repeatedly testing
Xvalues with the CDF_StudentsT function until it arrives at P value
that is within 1x10^{12} units from the specified Pvalue (this
usually takes between 3060 iterations). A Student’s T distribution with
1df is a Cauchy Distribution, and it approaches a Normal distribution
when DF>30. Various sources recommend using the Normal distribution if
DF>100.
a) Parameters:
 Pvalue: Number (0 >= p >= 1)
 Degrees of Freedom: Number > 0
b) Usages:
 From "Probability Distribution Calculator", select
"Quantile (IDF)" and Student’s T distribution.
 (Avenue): theProb = av.Run("Jennessent.DistFunc”,
{“IDF_StudentsT, {Pvalue, DF}})
 (Avenue): theProb =
av.Run("Jennessent.TableDistFunc”, {“IDF_StudentsT, {Pvalue, DF}})
 (Avenue): theProb =
av.Run("Jennessent.IDF_StudentsT", {Pvalue, DF})
c) Function: The IDF_StudentsT T Function is dependent
on whether the test value is positive or negative:

 IDF_Weibull:
This function takes the specified probability and returns the value X,
such that P(X) = Pvalue, given the Weibull distribution with the
specified Location, Scale and Shape parameters. The Standardized Weibull
Distribution is that with Location = 0 and Scale = 1. The 2Parameter
Weibull Distribution is that with Location = 0.
a) Parameters:
 Pvalue: Number (0 >= p >= 1)
 Location: Number
 Scale: Number > 0
 Shape: Number > 0
b) Usages:
 From "Probability Distribution Calculator", select
"Quantile (IDF)" and Weibull distribution.
 (Avenue): theProb = av.Run("Jennessent.DistFunc”,
{“IDF_Weibull, {Pvalue, Location, Scale, Number}})
 (Avenue): theProb =
av.Run("Jennessent.TableDistFunc”, {“IDF_Weibull, {Pvalue, Location,
Scale, Number}})
 (Avenue): theProb =
av.Run("Jennessent.IDF_Weibull", {Pvalue, Location, Scale, Number})
c) Function: 

Back to
Statistics/Distributions  Summary Statistics 
Probability
Calculators  References
Calculating
Summary Statistics with Avenue
Discussion of Distribution Functions:
Probability Density Functions  Cumulative Distribution Functions 
Quantile Functions
Download
Statistics Extension Manual
(Adobe PDF, version 5)
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