Package com.imsl.stat.distributions

Class LogNormalPD

java.lang.Object
com.imsl.stat.distributions.ProbabilityDistribution
com.imsl.stat.distributions.LogNormalPD
All Implemented Interfaces:
ClosedFormMaximumLikelihoodInterface, com.imsl.stat.distributions.MethodOfMomentsInterface, PDFGradientInterface, PDFHessianInterface, Serializable, Cloneable
public class LogNormalPD extends ProbabilityDistribution implements Serializable, Cloneable, PDFHessianInterface, ClosedFormMaximumLikelihoodInterface, com.imsl.stat.distributions.MethodOfMomentsInterface
The log-normal probability distribution.
See Also:

  • Constructor Details

    • LogNormalPD

      public LogNormalPD()
      Constructor for the log-normal probability distribution.

  • Method Details

    • getParameterLowerBounds

      public double[] getParameterLowerBounds()
      Returns the lower bounds of the parameters.
      Specified by:
      getParameterLowerBounds in class ProbabilityDistribution
      Returns:
      a double array of length 2 containing the lower bounds for \(\mu\in\mathbb{R}\) and \(\sigma\gt0\)

    • getParameterUpperBounds

      public double[] getParameterUpperBounds()
      Returns the upper bounds of the parameters.
      Specified by:
      getParameterUpperBounds in class ProbabilityDistribution
      Returns:
      a double array of length 2 containing the upper bounds for \(\mu\in\mathbb{R}\) and \(\sigma\gt0\)

    • pdf

      public double pdf(double x, double... params)
      Returns the value of the probability density function.

      The probability density function of the log-normal distribution is $$f\left(x\right)=\frac{1}{x\sigma\sqrt{2\pi}} {e^{-\frac{{(\ln{x}-\mu)}^2 }{2{\sigma}^2}}}$$ where \(\mu\) is a location parameter and \(\sigma > 0\) is the scale parameter.

      Specified by:
      pdf in class ProbabilityDistribution
      Parameters:
      x - a double, the value (quantile) at which to evaluate the pdf. x must be strictly positive.
      params - a double array containing the parameters. The parameters can also be given in the form pdf(x,a,b), where a=\(\mu\) and b=\(\sigma\) are scalars.
      Returns:
      a double, the probability density at x given the parameter values

    • getPDFGradient

      public double[] getPDFGradient(double x, double... params)
      Returns the analytic gradient of the pdf evaluated at x.
      Specified by:
      getPDFGradient in interface PDFGradientInterface
      Parameters:
      x - a double, the value (quantile) at which to evaluate the pdf. x must be strictly positive.
      params - a double array containing the parameters
      Returns:
      a double array containing the first partial derivatives of the pdf with respect to the parameters evaluated at x and the input values params

    • getPDFHessian

      public double[][] getPDFHessian(double x, double... params)
      Returns the analytic Hessian of the pdf evaluated at x.
      Specified by:
      getPDFHessian in interface PDFHessianInterface
      Parameters:
      x - a double, the value at which to evaluate the Hessian. x must be strictly positive.
      params - a double array containing the parameters, \(\mu\) and \(\sigma\).
      Returns:
      a double matrix containing the second partial derivatives of the pdf with respect to the parameters

    • getClosedFormMLE

      public double[] getClosedFormMLE(double[] x)
      Returns the closed form maximum likelihood estimates.
      Specified by:
      getClosedFormMLE in interface ClosedFormMaximumLikelihoodInterface
      Parameters:
      x - a double array containing the data
      Returns:
      a double array containing maximum likelihood estimates for \(\mu, \sigma\)

    • getClosedFormMlStandardError

      public double[] getClosedFormMlStandardError(double[] x)
      Returns the standard errors of the closed form maximum likelihood estimates.
      Specified by:
      getClosedFormMlStandardError in interface ClosedFormMaximumLikelihoodInterface
      Parameters:
      x - a double array containing the data
      Returns:
      a double array containing the standard errors for the estimates of \(\mu, \sigma\)

    • getMethodOfMomentsEstimates

      public double[] getMethodOfMomentsEstimates(double[] x)
      Returns the method-of-moments estimates given the sample data.
      Specified by:
      getMethodOfMomentsEstimates in interface com.imsl.stat.distributions.MethodOfMomentsInterface
      Parameters:
      x - a double array containing the data
      Returns:
      a double array containing method-of-moments estimates for \(\mu\) and \(\sigma\)