Distribution

Represent a univariate probability distribution and related noise model.

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Declaration

classdef (Abstract) Distribution

Overview

Distribution is the abstract base class for a univariate probability distribution with density \(p(z)\) and cumulative distribution \(F(z) = \int_{-\infty}^{z} p(\zeta)\,\mathrm{d}\zeta.\) Subclasses provide those distribution functions, and this base class adds percentile inversion, range-limited second-moment integrals, random sampling, correlated-noise generation, and goodness-of-fit diagnostics.

The method locationOfCDFPercentile returns \(z_{\alpha}\) satisfying \(F(z_{\alpha}) = \alpha.\) The method varianceInRange evaluates \(\int_{z_{\min}}^{z_{\max}} z^{2} p(z)\,\mathrm{d}z,\) which coincides with the variance contribution on that interval for centered distributions. The Anderson-Darling and Kolmogorov-Smirnov methods compare the empirical distribution of a sample against the theoretical CDF \(F(z)\) through standard AD and KS statistics.

Topics

• Inspect distribution properties
  • cdf Cumulative distribution function \(F(z)\).
  • distributionFromFile Initialize a persisted distribution from a NetCDF file.
  • distributionFromGroup Initialize a persisted distribution from a NetCDF group.
  • locationOfCDFPercentile Find the location of a CDF percentile.
  • logPDF Logarithm of the probability density \(\log p(z)\).
  • pdf Probability density function \(p(z)\).
  • sigma0 Initialization scale \(\sigma_0\) satisfying \(w(\sigma_0) = \sigma_0^2\).
  • variance Total variance.
  • varianceInPercentileRange Compute the second moment between two CDF percentiles.
  • varianceInRange Compute the range-limited second moment of the distribution.
  • w Weight function \(w(z)\) for residual-based reweighting.
  • writeToFile Write this distribution to a NetCDF file.
  • zrange Support interval \([z_{\min}, z_{\max}]\) for the distribution.
• Sample from distributions
  • rand Draw random samples from the distribution.
• Evaluate distribution fit
  • andersonDarlingError Compute the Anderson-Darling fit statistic for a sample.
  • andersonDarlingInterquartileError Compute an interquartile Anderson-Darling fit statistic.
  • kolmogorovSmirnovError Compute the Kolmogorov-Smirnov fit statistic for a sample.
  • kolmogorovSmirnovInterquartileError Compute an interquartile Kolmogorov-Smirnov fit statistic.
• Model correlated noise
  • noise Draw a correlated noise process on a lag grid.
  • rho Autocorrelation function \(\rho(\tau)\) used by noise.
• Developer
  • classDefinedPropertyAnnotations return array of WVPropertyAnnotation initialized by default
• Other
  • classRequiredPropertyNames
  • isequal

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