smile.stat.distribution

## Class LogNormalDistribution

• All Implemented Interfaces:
java.io.Serializable, 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.
Serialized Form
• ### Field Summary

Fields
Modifier and Type Field and Description
`double` `mu`
The mean of normal distribution.
`double` `sigma`
The standard deviation of normal distribution.
• ### Constructor Summary

Constructors
Constructor and Description
```LogNormalDistribution(double mu, double sigma)```
Constructor.
• ### Method Summary

All Methods
Modifier and Type Method and Description
`double` `cdf(double x)`
Cumulative distribution function.
`double` `entropy()`
Shannon entropy of the distribution.
`static LogNormalDistribution` `fit(double[] data)`
Estimates the distribution parameters by MLE.
`int` `length()`
The number of parameters of the distribution.
`double` `logp(double x)`
The density at x in log scale, which may prevents the underflow problem.
`double` `mean()`
The mean of 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.
`java.lang.String` `toString()`
`double` `variance()`
The variance of distribution.
• ### Methods inherited from class smile.stat.distribution.AbstractDistribution

`inverseTransformSampling, quantile, quantile, rejection`
• ### Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait`
• ### Methods inherited from interface smile.stat.distribution.Distribution

`likelihood, logLikelihood, rand, sd`
• ### Field Detail

• #### mu

`public final double mu`
The mean of normal distribution.
• #### sigma

`public final double sigma`
The standard deviation of normal distribution.
• ### Constructor Detail

• #### LogNormalDistribution

```public LogNormalDistribution(double mu,
double sigma)```
Constructor.
Parameters:
`mu` - the mean of normal distribution.
`sigma` - the standard deviation of normal distribution.
• ### Method Detail

• #### fit

`public static LogNormalDistribution fit(double[] data)`
Estimates the distribution parameters by MLE.
• #### length

`public int length()`
Description copied from interface: `Distribution`
The number of parameters of the distribution. The "length" is in the sense of the minimum description length principle.
• #### mean

`public double mean()`
Description copied from interface: `Distribution`
The mean of distribution.
• #### variance

`public double variance()`
Description copied from interface: `Distribution`
The variance of distribution.
• #### entropy

`public double entropy()`
Description copied from interface: `Distribution`
Shannon entropy of the distribution.
• #### toString

`public java.lang.String toString()`
Overrides:
`toString` in class `java.lang.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.