Dirac Delta Function https://en.wikipedia.org/wiki/Dirac_delta_function. More...
Inheritance diagram for MathPHP\Probability\Distribution\Continuous\DiracDelta:
Collaboration diagram for MathPHP\Probability\Distribution\Continuous\DiracDelta:
Public Member Functions | |
| const | __construct () |
| Constructor. | |
| pdf (float $x) | |
| Probability density function. More... | |
| cdf (float $x) | |
| Cumulative distribution function https://en.wikipedia.org/wiki/Heaviside_step_function. More... | |
| inverse (float $p) | |
| The inverse of the CDF function. More... | |
| mean () | |
| Mean of the distribution. More... | |
| median () | |
| Median of the distribution. More... | |
| mode () | |
| Mode 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 |
Detailed Description
Dirac Delta Function https://en.wikipedia.org/wiki/Dirac_delta_function.
Member Function Documentation
◆ cdf()
| MathPHP\Probability\Distribution\Continuous\DiracDelta::cdf | ( | float | $x | ) |
Cumulative distribution function https://en.wikipedia.org/wiki/Heaviside_step_function.
|+∞ | δ(x) dx = 1 |-∞
- Parameters
-
float $x
- Todo:
- how to handle x = 0, depending on context, some say CDF=.5 @ x=0
- Returns
- int
Implements MathPHP\Probability\Distribution\Continuous\ContinuousDistribution.
◆ inverse()
| MathPHP\Probability\Distribution\Continuous\DiracDelta::inverse | ( | float | $p | ) |
The inverse of the CDF function.
- Returns
- int
◆ mean()
| MathPHP\Probability\Distribution\Continuous\DiracDelta::mean | ( | ) |
Mean of the distribution.
- Returns
- int
Implements MathPHP\Probability\Distribution\Continuous\ContinuousDistribution.
◆ median()
| MathPHP\Probability\Distribution\Continuous\DiracDelta::median | ( | ) |
Median of the distribution.
- Returns
- int
◆ mode()
| MathPHP\Probability\Distribution\Continuous\DiracDelta::mode | ( | ) |
Mode of the distribution.
- Returns
- int
◆ pdf()
| MathPHP\Probability\Distribution\Continuous\DiracDelta::pdf | ( | float | $x | ) |
Probability density function.
/‾ | +∞, x = 0 δ(x) = < | 0, x ≠ 0 _
- Parameters
-
float $x
- Returns
- float probability
Implements MathPHP\Probability\Distribution\Continuous\ContinuousDistribution.
Member Data Documentation
◆ SUPPORT_LIMITS
| const MathPHP\Probability\Distribution\Continuous\DiracDelta::SUPPORT_LIMITS |
Initial value:
= [
'x' => '(-∞,∞)'
The documentation for this class was generated from the following file:
- src/Probability/Distribution/Continuous/DiracDelta.php
