geopdf

Geometric probability density function

Syntax

y = geopdf(x,p)

Description

y = geopdf(x,p) returns the probability density function (pdf) of the geometric distribution, evaluated at each value in x using the corresponding probabilities in p. The parameter p is the probability of success in any given trial, and x is the number of failures before the first success.

Examples

Compute and Plot Geometric Probability Density Function

Compute the probability density function (pdf) of the geometric distribution with a probability of success p=0.25, for integer values between 0 and 20.

x = 0:1:20;
p = 0.25;
y = geopdf(x,p);

Plot the pdf. Use blue circle markers.

plot(x,y,"o",MarkerFaceColor="b")
grid on
xlabel("x")
ylabel("y")

The plot indicates that there is approximately a 14% chance of experiencing exactly two failures before the first success.

Compute Geometric Distribution pdf

Suppose you toss a fair coin repeatedly, and a success occurs when the coin lands with heads facing up. What is the probability of observing exactly three tails (failures) before tossing heads?

Determine the value of the probability density function (pdf) for the geometric distribution at x equal to 3. The probability of success (tossing heads) p in any given trial is 0.5.

x = 3;
p = 0.5;
y = geopdf(x,p)

y = 
0.0625

The returned value of y indicates that the probability of observing exactly three tails before tossing heads is 0.0625.

Input Arguments

x — Values at which to evaluate pdf

nonnegative integer scalar | array of nonnegative integer scalars

Values at which to evaluate the pdf, specified as a nonnegative integer scalar or an array of nonnegative integer scalars. x is the number of failures before the first success.

To evaluate the pdf at multiple values, specify x using an array. To evaluate the pdfs of multiple distributions, specify p using an array. If both input arguments x and p are arrays, then the array sizes must be the same. If only one of the input arguments is an array, then geopdf expands the scalar input into a constant array of the same size as the array input. Each element in y is the pdf value of the distribution specified by the corresponding element in p, evaluated at the corresponding element in x.

Data Types: single | double

p — Probability of success

scalar in the range [0,1] | array of scalars in the range [0,1]

Probability of success in any given trial, specified as a scalar or an array of scalars in the range [0,1].

To evaluate the pdf at multiple values, specify x using an array. To evaluate the pdfs of multiple distributions, specify p using an array. If both input arguments x and p are arrays, then the array sizes must be the same. If only one of the input arguments is an array, then geopdf expands the scalar input into a constant array of the same size as the array input. Each element in y is the pdf value of the distribution specified by the corresponding element in p, evaluated at the corresponding element in x.

Data Types: single | double

Output Arguments

y — Geometric pdf values

scalar in the range [0,1] | array of scalars in the range [0,1]

Geometric pdf values, returned as a scalar or an array of scalars in the range [0,1]. y is the same size as x and p after any necessary scalar expansion.

More About

Geometric Distribution pdf

The probability density function (pdf) of the geometric distribution is

$$y=f(x|p)=p{(1-p)}^x;x=0,1,2,\dots ,$$

where p is the probability of success, and x is the number of failures before the first success. The result y is the probability of observing exactly x trials before a success, when the probability of success in any given trial is p. For discrete distributions, the pdf is also known as the probability mass function (pmf).

For more information, see Geometric Distribution.

Alternative Functionality

• geopdf is a function specific to the geometric distribution. Statistics and Machine Learning Toolbox™ also offers the generic function pdf, which supports various probability distributions. To use pdf, specify the probability distribution name and its parameters. Note that the distribution-specific function geopdf is faster than the generic function pdf.

• Use the Probability Distribution Function Tool to create an interactive plot of the cumulative distribution function (cdf) or probability density function (pdf) for a probability distribution.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced before R2006a