truncate

Truncate probability distribution object

Syntax

t = truncate(pd,lower,upper)

Description

t = truncate(pd,lower,upper) returns a probability distribution t, which is the probability distribution pd truncated to the specified interval with lower limit, lower, and upper limit, upper.

Examples

Truncate a Probability Distribution

Create a standard normal probability distribution object.

pd = makedist('Normal')

pd = 
  NormalDistribution

  Normal distribution
       mu = 0
    sigma = 1

Truncate the distribution to have a lower limit of -2 and an upper limit of 2.

t = truncate(pd,-2,2)

t = 
  NormalDistribution

  Normal distribution
       mu = 0
    sigma = 1
  Truncated to the interval [-2, 2]

Plot the pdf of the original and truncated distributions for a visual comparison.

x = linspace(-3,3,1000);
figure
plot(x,pdf(pd,x))
hold on
plot(x,pdf(t,x),'LineStyle','--')
legend('Normal','Truncated')
hold off

Generate Random Numbers from a Truncated Distribution

Create a standard normal probability distribution object.

pd = makedist('Normal')

pd = 
  NormalDistribution

  Normal distribution
       mu = 0
    sigma = 1

Truncate the distribution by restricting it to positive values. Set the lower limit to 0 and the upper limit to infinity.

t = truncate(pd,0,inf)

t = 
  NormalDistribution

  Normal distribution
       mu = 0
    sigma = 1
  Truncated to the interval [0, Inf]

Generate random numbers from the truncated distribution and visualize with a histogram.

r = random(t,10000,1);
histogram(r,100)

Input Arguments

pd — Probability distribution

probability distribution object

Probability distribution, specified as a probability distribution object.

Create a probability distribution object with specified parameter values using makedist.

Alternatively, for a fittable distribution, create a probability distribution object by fitting it to data using fitdist or the Distribution Fitter app.

lower — Lower truncation limit

scalar value

Lower truncation limit, specified as a scalar value.

Data Types: single | double

upper — Upper truncation limit

scalar value

Upper truncation limit, specified as a scalar value.

Data Types: single | double

Output Arguments

t — Truncated distribution

probability distribution object

Truncated distribution, returned as a probability distribution object. The probability distribution function (pdf) of t is 0 outside the truncation interval. Inside the truncation interval, the pdf of t is equal to the pdf of pd, but divided by the probability assigned to that interval by pd.

The object properties of t are the same as those of pd with these exceptions:

• The Truncation property of t stores the truncation interval.

• The IsTruncated property of t is 1.

• The InputData property of t is empty. For a fitted distribution object, the InputData property stores the data used for distribution fitting. The truncated distribution object does not store the input data.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• The input argument pd can be a fitted probability distribution object for beta, exponential, extreme value, lognormal, normal, and Weibull distributions. Create pd by fitting a probability distribution to sample data from the fitdist function. For an example, see Code Generation for Probability Distribution Objects.

• A truncated probability distribution object cannot be an input argument of an entry-point function. To evaluate a truncated distribution using object functions such as cdf, pdf, mean, and so on, call truncate and one or more of these object functions within a single entry-point function.

For more information on code generation, see Introduction to Code Generation and General Code Generation Workflow.