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HalfNormalDistribution

Half-normal probability distribution object

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Description

AHalfNormalDistributionobject consists of parameters, a model description, and sample data for a half-normal probability distribution.

half-normal分布是一个特例the folded normal and truncated normal distribution. Applications of the half-normal distribution include modeling measurement data and lifetime data.

The half-normal distribution uses the following parameters:

Parameter Description 金宝app
mu Location − ∞ < μ < ∞
sigma Scale σ ≥ 0

For more information about the half-normal distribution, seeHalf-Normal Distribution.

Creation

There are several ways to create aHalfNormalDistributionprobability distribution object.

  • Create a distribution with specified parameter values usingmakedist.

  • Fit a distribution to data usingfitdist.

  • Interactively fit a distribution to data using theDistribution Fitter应用程序。

Properties

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Distribution Parameters

Location parameter of the half-normal distribution, specified as a scalar value. Themuparameter is also the lower limit of the half-normal distribution.

The Statistics and Machine Learning Toolbox™ implementation of the half-normal distribution assumes a fixed value for the location parameterμ. You can specify a value for theμparameter when creating aHalfNormalDistributionobject.

Data Types:single|double

Scale parameter of the half-normal distribution, specified as a nonnegative scalar value.

Data Types:single|double

Distribution Characteristics

This property is read-only.

Logical flag for truncated distribution, specified as a logical value. IfIsTruncatedequals0, the distribution is not truncated. IfIsTruncatedequals1, the distribution is truncated.

Data Types:logical

This property is read-only.

Number of parameters for the probability distribution, specified as a positive integer value.

Data Types:double

This property is read-only.

Covariance matrix of the parameter estimates, specified as ap-by-pmatrix, wherepis the number of parameters in the distribution. The (i,j) element is the covariance between the estimates of theith parameter and thejth parameter. The (i,i) element is the estimated variance of theith parameter. If parameteriis fixed rather than estimated by fitting the distribution to data, then the (i,i) elements of the covariance matrix are 0.

Data Types:double

This property is read-only.

Logical flag for fixed parameters, specified as an array of logical values. If0, the corresponding parameter in theParameterNamesarray is not fixed. If1, the corresponding parameter in theParameterNamesarray is fixed.

Data Types:logical

This property is read-only.

Distribution parameter values, specified as a vector.

Data Types:single|double

This property is read-only.

Truncation interval for the probability distribution, specified as a vector containing the lower and upper truncation boundaries.

Data Types:single|double

Other Object Properties

This property is read-only.

Probability distribution name, specified as a character vector.

Data Types:char

This property is read-only.

Data used for distribution fitting, specified as a structure containing the following:

  • data: Data vector used for distribution fitting.

  • cens: Censoring vector, or empty if none.

  • freq: Frequency vector, or empty if none.

Data Types:struct

This property is read-only.

Distribution parameter descriptions, specified as a cell array of character vectors. Each cell contains a short description of one distribution parameter.

Data Types:char

This property is read-only.

Distribution parameter names, specified as a cell array of character vectors.

Data Types:char

Object Functions

cdf Cumulative distribution function
icdf Inverse cumulative distribution function
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative loglikelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density function
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution

Examples

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Open Live Script 
pd = makedist('HalfNormal')
pd = HalfNormalDistribution Half Normal distribution mu = 0 sigma = 1
Open Live Script

Create a half-normal distribution object. Specifymuequal to 0 andsigmaequal to 1.5.

pd = makedist('HalfNormal','mu',0,'sigma',1.5)
pd = HalfNormalDistribution Half Normal distribution mu = 0 sigma = 1.5

Compute the mean and standard deviation of the distribution.

m = mean(pd)
m = 1.1968
s = std(pd)
s = 0.9042
Open Live Script

Generate 100 random numbers from a standard normal distribution and compute their absolute value.

rngdefault% For reproducibilityx = abs(random(makedist('Normal'),100,1));

Fit a half-normal distribution object to the sample data.

pd = fitdist(x,'HalfNormal')
pd = HalfNormalDistribution Half Normal distribution mu = 0 sigma = 1.1631 [1.02184, 1.35006]

计算安装half-normal的均值distribution using the probability distribution object.

m = mean(pd)
m = 0.9280

Calculate the mean of the half-normal distribution by substituting the fittedmuandsigmaparameter values into the formula

m e a n = μ + σ 2 π . 

mcalc = pd.mu + pd.sigma*(sqrt(2/pi))
mcalc = 0.9280

References

[1] Cooray, K. and M.M.A. Ananda. “A Generalization of the Half-Normal Distribution with Applications to Lifetime Data.”Communications in Statistics – Theory and Methods. Vol. 37, Number 9, 2008, pp. 1323–1337.

[2] Pewsey, A.Large-Sample Inference for the General Half-Normal Distribution.Communications in Statistics – Theory and Methods. Vol. 31, Number 7, 2002, pp. 1045–1054.

See Also

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Topics

Introduced in R2016a

Statistics and Machine Learning Toolbox Documentation

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