Introduction:
Explore different distributions (normal, poisson, student,exponential) using matlab.
Normal distribution
- normrnd = Normal random numbers
r = normrnd(mu,sigma) generates a random number from the normal distribution with mean parameter mu and standard deviation parameter sigma.
r = normrnd(mu,sigma,sz1,...,szN) generates an array of normal random numbers, where sz1,...,szN indicates the size of each dimension.
Arguments:
mu — Mean
sigma — Standard deviation
- More on normal distribution on a separate article
Poisson distribution
poissrnd = generates random numbers from Poisson distribution.
r = poissrnd(lambda) generates random numbers from the Poisson distribution specified by the rate parameter lambda.
lambda can be a scalar, vector, matrix, or multidimensional array.
- r = poissrnd(lambda,sz1,...,szN) generates an array of random numbers from the Poisson distribution with the scalar rate parameter lambda, where sz1,...,szN indicates the size of each dimension.
Examples:
1)
r_scalar = poissrnd(20)
r_scalar = 9
2)
Generate a 2-by-3 array of random numbers from the same distribution by specifying the required array dimensions.
lambda = 20
r_array = poissrnd(lambda ,2,3)
r_array = 2×3
13 14 18
26 16 21
3)
lambda = 10:2:20
lambda = 1×6
10 12 14 16 18 20
Generate random numbers from the Poisson distributions.
r = poissrnd(lambda)
r = 1×6
14 13 14 9 14 31
- poisspdf= Poisson probability density function
Parameters:
x — Values at which to evaluate Poisson pdf
lambda — Rate parameters
Compute the Poisson probability density function values at each value from 0 to 10. These values correspond to the probabilities that a disk has 0, 1, 2, .., 10 flaws.
Examples:
1)
flaws = 0:10;
y = poisspdf(flaws,2);
2)
tV = [0:100]';
lambda = 10;
pois = poisspdf(tV,lambda);
Student's distribution
- tcdf = Student's t cumulative distribution function
p = tcdf(x,nu) returns the cumulative distribution function (cdf) of the Student's t distribution with nu degrees of freedom, evaluated at the values in x.
Arguments:
x — Values at which to evaluate cdf
nu — Degrees of freedom
- tinv = Student's t inverse cumulative distribution function
Examples:
1)
Find the 95th percentile of the Student's t distribution with 50 degrees of freedom.
p = .95;
nu = 50;
x = tinv(p,nu)
x = 1.6759
Exponential distribution
- exprnd = calculates exponential random numbers
Examples:
1)
r = exprnd(mu)
r = exprnd(mu) generates a random number from the exponential distribution with mean mu.
2)
r = exprnd(mu,sz1,...,szN)
generates an array of random numbers from the exponential distribution, where sz1,...,szN indicates the size of each dimension.
- exppdf = Exponential probability density function
1) y = exppdf(x) returns the probability density function (pdf) of the standard exponential distribution, evaluated at the values in x.
Compute the density of the value 5 in the standard exponential distribution.
y1 = exppdf(5)
y1 = 0.0067
2) y = exppdf(x,mu) returns the pdf of the exponential distribution with mean mu, evaluated at the values in x.
Compute the density of the value 5 in the exponential distributions specified by means 1 through 5.
y2 = exppdf(5,1:5)
y2 = 1×5
0.0067 0.0410 0.0630 0.0716 0.0736
Arguments:
x — Values at which to evaluate pdf
mu — mean
Histograms
1) histogram = Histogram plot
2) histfit = Histogram with a distribution fit
histfit(data) plots a histogram of values in data using the number of bins equal to the square root of the number of elements in data and fits a normal density function.
Construct a histogram with a normal distribution fit.
(bins are the number of bars you will see in your hist)
r = normrnd(10,1,100,1);
histfit(r)
example
histfit(data,nbins) plots a histogram using nbins bins and fits a normal density function.
Construct a histogram using six bins with a normal distribution fit.
r = normrnd(10,1,100,1);
histfit(r,6)
Clearing environment
- clc = clears command window
- clear = Remove items from workspace, freeing up system memory
General Useful Commands
- mean = calculates average or mean value of array
- nargin = returns the number of function input arguments
- ttest = One-sample and paired-sample t-test
More on ttest
The one-sample t-test is a parametric test of the location parameter when the population standard deviation is unknown.
The test statistic is:
t= (x−μ)/(s/squar(n))
where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size. Under the null hypothesis, the test statistic has Student’s t distribution with n – 1 degrees of freedom.
Arguments of ttest:
1)
Alpha — Significance level
0.05 (default) | scalar value in the range (0,1)
2)
Dim — Dimension
first nonsingleton dimension (default) | positive integer value
Dimension of the input matrix along which to test the means consisting of 'Dim' and a positive integer value. For example, specifying 'Dim',1 tests the column means, while 'Dim',2 tests the row means.
3)
Tail — Type of alternative hypothesis
'both' (default) | 'right' | 'left'
Type of alternative hypothesis to evaluate, specified as the comma-separated pair consisting of 'Tail' and one of:
'both' — Test against the alternative hypothesis that the population mean is not m.
'right' — Test against the alternative hypothesis that the population mean is greater than m.
'left' — Test against the alternative hypothesis that the population mean is less than m.
Output Arguments of ttest:
1)
Hypothesis test result
Hypothesis test result, returned as 1 or 0.
If h = 1, this indicates the rejection of the null hypothesis at the Alpha significance level.
If h = 0, this indicates a failure to reject the null hypothesis at the Alpha significance level.
2)
p — p-value,scalar value in the range [0,1]
p-value of the test, returned as a scalar value in the range [0,1]. p is the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. Small values of p cast doubt on the validity of the null hypothesis.
3)
ci — Confidence interval
vector
Confidence interval for the true population mean, returned as a two-element vector containing the lower and upper boundaries of the 100 × (1 – Alpha)% confidence interval.
4)
stats — Test statistics
structure
Test statistics, returned as a structure containing the following:
tstat — Value of the test statistic.
df — Degrees of freedom of the test.
sd — Estimated population standard deviation. For a paired t-test, sd is the standard deviation of x – y.
Top comments (0)