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# Matlab: Statistics and Distributions

## on Jan 08, 2010

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Statistics and Distributions using Matlab

Statistics and Distributions using Matlab

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## Matlab: Statistics and DistributionsPresentation Transcript

• Distributions
• Probability Distributions
Wikipedia: A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous). The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.
• Types of supported distributions
pdf — Probability density functions
cdf — Cumulative distribution functions
inv — Inverse cumulative distribution functions
stat — Distribution statistics functions
fit — Distribution fitting functions
like — Negative log-likelihood functions
rnd — Random number generators
• Supported Distributions
Bernoulli Distribution
Beta Distribution
Binomial Distribution
Birnbaum-Saunders Distribution
Chi-Square Distribution
Copulas
• Geometric Distribution
• Hypergeometric Distribution
• Inverse Gaussian Distribution
• Inverse Wishart Distribution
• Johnson System
• Logistic Distribution
• Loglogistic Distribution
• Custom Distributions
• Exponential Distribution
• Extreme Value
• Distribution
• F Distribution
• Gamma Distribution
• Gaussian Distribution
• Gaussian Mixture Distributions
• Generalized Extreme Value Distribution
• Generalized Pareto Distribution
• Supported Distributions
Lognormal Distribution
Multinomial Distribution
Multivariate Gaussian Distribution
Multivariate Normal Distribution
Multivariate t Distribution
Nakagami Distribution
Negative Binomial Distribution
Noncentral Chi-Square Distribution
Noncentral F Distribution
Noncentral t Distribution
Nonparametric Distributions
• Normal Distribution
• Pareto Distribution
• Pearson System
• Piecewise Distributions
• Poisson Distribution
• Rayleigh Distribution
• Rician Distribution
• Student's t Distribution
• t Location-Scale Distribution
• Uniform Distribution (Continuous)
• Uniform Distribution (Discrete)
• Weibull Distribution
• Wishart Distribution
• Probability Density functions
Parametric Estimation
Nonparametric Estimation
• 1. Parametric estimation
• p = 0.2; % Probability of success for each trial
• n = 10; % Number of trials
• k = 0:n; % Outcomes
• m = binopdf(k,n,p); % Probability mass vector
• bar(k,m) % Visualize the probability distribution
• set(get(gca,'Children'),'FaceColor',[.8 .8 1])
• grid on
• 1. Parametric estimation
• 2. Non parametric estimation
A distribution of data can be described graphically with a histogram:
• MPG = cars.MPG;
• hist(MPG)
• set(get(gca,'Children'),'FaceColor',[.8 .8 1])
• 2. Non parametric estimation
• 2. Non parametric estimation
You can also describe a data distribution by estimating its density. The ksdensity function does this using a kernel smoothing method. A nonparametric density estimate of the data above, using the default kernel and bandwidth, is given by:
• [f,x] = ksdensity(MPG);
• plot(x,f);
• title('Density estimate for MPG') ;
• 2. Non parametric estimation
• Cumulative Distribution Functions
Parametric Estimation
Nonparametric Estimation
• Inverse Cumulative Distribution Functions
Each function in this family represents a parametric family of distributions. Input arguments are arrays of cumulative probabilities between 0 and 1 followed by a list of parameter values specifying a particular member of the distribution family.
• Inverse Cumulative Distribution Functions
The expinv function can be used to compute inverses of exponential cumulative probabilities:
• Distribution Statistics Functions
Each function in this family represents a parametric family of distributions. Input arguments are lists of parameter values specifying a particular member of the distribution family. Functions return the mean and variance of the distribution, as a function of the parameters.
• Distribution Statistics Functions
For example, the wblstat function can be used to visualize the mean of the Weibull distribution as a function of its two distribution parameters:
• a = 0.5:0.1:3;
• b = 0.5:0.1:3;
• [A,B] = meshgrid(a,b);
• M = wblstat(A,B);
• surfc(A,B,M)
• Distribution Statistics Functions
• Distribution Fitting Functions
Fitting Supported Distributions
Fitting Piecewise Distributions
• Negative Log-Likelihood Functions
Each function in this family represents a parametric family of distributions. Input arguments are lists of parameter values specifying a particular member of the distribution family followed by an array of data. Functions return the negative log-likelihood of the parameters, given the data.
• Random Number Generators
Each RNG represents a parametric family of distributions. Input arguments are lists of parameter values specifying a particular member of the distribution family followed by the dimensions of an array. RNGs return random numbers from the specified distribution in an array of the specified dimensions.
• Visit more self help tutorials
Pick a tutorial of your choice and browse through it at your own pace.
The tutorials section is free, self-guiding and will not involve any additional support.
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