Normal probability distribution object
NormalDistribution object consists of parameters, a model
description, and sample data for a normal probability distribution.
The normal distribution, sometimes called the Gaussian distribution, is a two-parameter family of curves. The usual justification for using the normal distribution for modeling is the Central Limit theorem, which states (roughly) that the sum of independent samples from any distribution with finite mean and variance converges to the normal distribution as the sample size goes to infinity.
The normal distribution uses the following parameters.
There are several ways to create a
Mean of the normal distribution, specified as a scalar value.
sigma— Standard deviation
Standard deviation of the normal distribution, specified as a nonnegative scalar value.
You can specify
sigma to be zero when you create an
object by using
makedist. Some object
functions support an object
pd with zero standard
deviation. For example,
(pd) always returns
(pd,x) returns either 0 or 1. The
output is 0 if
x is smaller than
mu, and 1 otherwise.
var return the mean,
standard deviation, and variance of
|Cumulative distribution function|
|Inverse cumulative distribution function|
|Mean of probability distribution|
|Median of probability distribution|
|Negative loglikelihood of probability distribution|
|Confidence intervals for probability distribution parameters|
|Probability density function|
|Profile likelihood function for probability distribution|
|Standard deviation of probability distribution|
|Truncate probability distribution object|
|Variance of probability distribution|
Create a normal distribution object using the default parameter values.
pd = makedist('Normal')
pd = NormalDistribution Normal distribution mu = 0 sigma = 1
Create a normal distribution object by specifying the parameter values.
pd = makedist('Normal','mu',75,'sigma',10)
pd = NormalDistribution Normal distribution mu = 75 sigma = 10
Compute the interquartile range of the distribution.
r = iqr(pd)
r = 13.4898
Load the sample data and create a vector containing the first column of student exam grade data.
load examgrades x = grades(:,1);
Create a normal distribution object by fitting it to the data.
pd = fitdist(x,'Normal')
pd = NormalDistribution Normal distribution mu = 75.0083 [73.4321, 76.5846] sigma = 8.7202 [7.7391, 9.98843]
The intervals next to the parameter estimates are the 95% confidence intervals for the distribution parameters.
Usage notes and limitations:
You must create a probability distribution object by fitting a
probability distribution to sample data from the
fitdist function. For the usage notes and limitations of
fitdist, see Code Generation of
For more information on code generation, see Introduction to Code Generation and Code Generation for Probability Distribution Objects.