LogNormalDistribution (Smile Math 1.0.3 API)

java.lang.Object
- smile.stat.distribution.AbstractDistribution
- - smile.stat.distribution.LogNormalDistribution

All Implemented Interfaces:

Distribution
```
public class LogNormalDistribution
extends AbstractDistribution
```
A log-normal distribution is a probability distribution of a random variable whose logarithm is normally distributed. The log-normal distribution is the single-tailed probability distribution of any random variable whose logarithm is normally distributed. If X is a random variable with a normal distribution, then Y = exp(X) has a log-normal distribution; likewise, if Y is log-normally distributed, then log(Y) is normally distributed. A variable might be modeled as log-normal if it can be thought of as the multiplicative product of many independent random variables each of which is positive.

Author:

Haifeng Li

Constructor Summary

Constructors
Constructor and Description

LogNormalDistribution(double[] data)
Constructor.

LogNormalDistribution(double mu, double sigma)
Constructor.

Constructors
Constructor and Description
`LogNormalDistribution(double[] data)` Constructor.
`LogNormalDistribution(double mu, double sigma)` Constructor.

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`cdf(double x)` Cumulative distribution function.
`double`	`entropy()` Shannon entropy of the distribution.
`double`	`getMu()` Returns the parameter mu, which is the mean of normal distribution log(X).
`double`	`getSigma()` Returns the parameter sigma, which is the standard deviation of normal distribution log(X).
`double`	`logp(double x)` The density at x in log scale, which may prevents the underflow problem.
`double`	`mean()` The mean of distribution.
`int`	`npara()` The number of parameters of the distribution.
`double`	`p(double x)` The probability density function for continuous distribution or probability mass function for discrete distribution at x.
`double`	`quantile(double p)` The quantile, the probability to the left of quantile is p.
`double`	`rand()` Generates a random number following this distribution.
`double`	`sd()` The standard deviation of distribution.
`String`	`toString()`
`double`	`var()` The variance of distribution.

Methods inherited from class smile.stat.distribution.AbstractDistribution
inverseTransformSampling, likelihood, logLikelihood, quantile, quantile, rejection

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - LogNormalDistribution
```
public LogNormalDistribution(double mu,
                     double sigma)
```
    Constructor.
  - LogNormalDistribution
```
public LogNormalDistribution(double[] data)
```
    Constructor. Parameter will be estimated from the data by MLE.
- Method Detail
  - getMu
```
public double getMu()
```
    Returns the parameter mu, which is the mean of normal distribution log(X).
  - getSigma
```
public double getSigma()
```
    Returns the parameter sigma, which is the standard deviation of normal distribution log(X).
  - npara
```
public int npara()
```
    Description copied from interface: Distribution
    
    The number of parameters of the distribution.
  - mean
```
public double mean()
```
    Description copied from interface: Distribution
    
    The mean of distribution.
  - var
```
public double var()
```
    Description copied from interface: Distribution
    
    The variance of distribution.
  - sd
```
public double sd()
```
    Description copied from interface: Distribution
    
    The standard deviation of distribution.
  - entropy
```
public double entropy()
```
    Description copied from interface: Distribution
    
    Shannon entropy of the distribution.
  - toString
```
public String toString()
```
    Overrides:
    
    toString in class Object
  - rand
```
public double rand()
```
    Description copied from interface: Distribution
    
    Generates a random number following this distribution.
  - p
```
public double p(double x)
```
    Description copied from interface: Distribution
    
    The probability density function for continuous distribution or probability mass function for discrete distribution at x.
  - logp
```
public double logp(double x)
```
    Description copied from interface: Distribution
    
    The density at x in log scale, which may prevents the underflow problem.
  - cdf
```
public double cdf(double x)
```
    Description copied from interface: Distribution
    
    Cumulative distribution function. That is the probability to the left of x.
  - quantile
```
public double quantile(double p)
```
    Description copied from interface: Distribution
    
    The quantile, the probability to the left of quantile is p. It is actually the inverse of cdf.

Class LogNormalDistribution

Constructor Summary

Method Summary

Methods inherited from class smile.stat.distribution.AbstractDistribution

Methods inherited from class java.lang.Object

Constructor Detail

LogNormalDistribution

LogNormalDistribution

Method Detail

getMu

getSigma

npara

mean

var

sd

entropy

toString

rand

p

logp

cdf

quantile