Struct LogNormal 

pub struct LogNormal { /* private fields */ }

Log-normal distribution: if X ~ LogNormal(μ, σ), then ln(X) ~ N(μ, σ²).

Mathematical Definition

• PDF: (1/(xσ√(2π))) exp(−(ln(x)−μ)²/(2σ²)) for x > 0
• CDF: Φ((ln(x)−μ)/σ)
• Mean: exp(μ + σ²/2)
• Variance: (exp(σ²) − 1) · exp(2μ + σ²)

Reference: Johnson, Kotz & Balakrishnan (1994), Continuous Univariate Distributions, Vol. 1, Chapter 14.

Implementations

impl LogNormal

pub fn new(mu: f64, sigma: f64) -> Result<Self, DistributionError>

Creates a new log-normal distribution.

Parameters mu and sigma are the mean and std dev of ln(X).

Errors

Returns Err if sigma ≤ 0 or parameters are not finite.

pub fn mu(&self) -> f64

pub fn sigma(&self) -> f64

pub fn mean(&self) -> f64

Mean = exp(μ + σ²/2).

pub fn variance(&self) -> f64

Variance = (exp(σ²) − 1) · exp(2μ + σ²).

pub fn pdf(&self, x: f64) -> f64

PDF for x > 0.

pub fn cdf(&self, x: f64) -> f64

CDF: Φ((ln(x)−μ)/σ) for x > 0.

pub fn quantile(&self, p: f64) -> Option<f64>

Inverse CDF: exp(μ + σ·Φ⁻¹(p)).

Returns None if p is outside (0, 1).

Trait Implementations

impl Clone for LogNormal

fn clone(&self) -> LogNormal

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for LogNormal

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl PartialEq for LogNormal

fn eq(&self, other: &LogNormal) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl StructuralPartialEq for LogNormal