Exponential distribution https://en.wikipedia.org/wiki/Exponential_distribution. More...
Inheritance diagram for MathPHP\Probability\Distribution\Continuous\Exponential:
Collaboration diagram for MathPHP\Probability\Distribution\Continuous\Exponential:
Public Member Functions | |
| __construct (float $λ) | |
| Constructor. More... | |
| pdf (float $x) | |
| Probability density function. More... | |
| cdf (float $x) | |
| Cumulative distribution function. More... | |
| inverse (float $p) | |
| Inverse cumulative distribution function (quantile function) More... | |
| mean () | |
| Mean of the distribution. More... | |
| median () | |
| Median of the distribution. More... | |
| mode () | |
| Mode of the distribution. More... | |
| variance () | |
| Variance of the distribution. More... | |
 Public Member Functions inherited from MathPHP\Probability\Distribution\Continuous\Continuous | |
| inverse (float $target) | |
| The Inverse CDF of the distribution. More... | |
| between (float $x₁, float $x₂) | |
| CDF between - probability of being between two points, x₁ and x₂ The area under a continuous distribution, that lies between two specified points. More... | |
| outside (float $x₁, float $x₂) | |
| CDF outside - Probability of being below x₁ and above x₂. More... | |
| above (float $x) | |
| CDF above - Probability of being above x to ∞ Area under a continuous distribution, that lies above a specified point. More... | |
| rand () | |
| Produce a random number with a particular distribution. More... | |
| Public Member Functions inherited from MathPHP\Probability\Distribution\Distribution | |
| __construct (... $params) | |
| Constructor. More... | |
Public Attributes | |
| const | PARAMETER_LIMITS |
| const | SUPPORT_LIMITS |
| Public Attributes inherited from MathPHP\Probability\Distribution\Continuous\Continuous | |
| const | GUESS_THRESHOLD = 10 |
| const | GUESS_ALLOWANCE = 8 |
Protected Attributes | |
| $λ | |
Detailed Description
Constructor & Destructor Documentation
◆ __construct()
| MathPHP\Probability\Distribution\Continuous\Exponential::__construct | ( | float | $λ | ) |
Constructor.
- Parameters
-
float $λ often called the rate parameter
Member Function Documentation
◆ cdf()
| MathPHP\Probability\Distribution\Continuous\Exponential::cdf | ( | float | $x | ) |
Cumulative distribution function.
f(x;λ) = 1 − ℯ^⁻λx x ≥ 0 = 0 x < 0
- Parameters
-
float $x the random variable
- Returns
- float
Implements MathPHP\Probability\Distribution\Continuous\ContinuousDistribution.
◆ inverse()
| MathPHP\Probability\Distribution\Continuous\Exponential::inverse | ( | float | $p | ) |
Inverse cumulative distribution function (quantile function)
−ln(1 − p) F⁻¹(p;λ) = -------— 0 ≤ p < 1 λ
- Parameters
-
float $p
- Returns
- float
- Exceptions
-
OutOfBoundsException
◆ mean()
| MathPHP\Probability\Distribution\Continuous\Exponential::mean | ( | ) |
Mean of the distribution.
μ = λ⁻¹
- Returns
- float
Implements MathPHP\Probability\Distribution\Continuous\ContinuousDistribution.
◆ median()
| MathPHP\Probability\Distribution\Continuous\Exponential::median | ( | ) |
Median of the distribution.
ln(2) median = --— λ
- Returns
- float
◆ mode()
| MathPHP\Probability\Distribution\Continuous\Exponential::mode | ( | ) |
Mode of the distribution.
mode = 0
- Returns
- float
◆ pdf()
| MathPHP\Probability\Distribution\Continuous\Exponential::pdf | ( | float | $x | ) |
Probability density function.
f(x;λ) = λℯ^⁻λx x ≥ 0 = 0 x < 0
- Parameters
-
float $x the random variable
- Returns
- float
Implements MathPHP\Probability\Distribution\Continuous\ContinuousDistribution.
◆ variance()
| MathPHP\Probability\Distribution\Continuous\Exponential::variance | ( | ) |
Variance of the distribution.
1 var[X] = – λ²
- Returns
- float
Member Data Documentation
◆ PARAMETER_LIMITS
| const MathPHP\Probability\Distribution\Continuous\Exponential::PARAMETER_LIMITS |
Initial value:
= [
'λ' => '(0,∞)'
◆ SUPPORT_LIMITS
| const MathPHP\Probability\Distribution\Continuous\Exponential::SUPPORT_LIMITS |
Initial value:
= [
'x' => '[0,∞)'
The documentation for this class was generated from the following file:
- src/Probability/Distribution/Continuous/Exponential.php
