JKQTPlotter trunk/v5.0.0
an extensive Qt5+Qt6 Plotter framework (including a feature-richt plotter widget, a speed-optimized, but limited variant and a LaTeX equation renderer!), written fully in C/C++ and without external dependencies
Loading...
Searching...
No Matches
Functions
Kernels for 1-dimensional Histograms
JKQTMath: Special Math and Statistics Utilities » Statistical Computations » 1-dimensional Kernel Density Estimates
Collaboration diagram for Kernels for 1-dimensional Histograms:

Functions

double jkqtpstatKernel1DCauchy (double t)
 a 1D Cauchy kernel function, e.g. for Kernel Density Estimation
 
double jkqtpstatKernel1DCosine (double t)
 a 1D cosine kernel function, e.g. for Kernel Density Estimation
 
double jkqtpstatKernel1DEpanechnikov (double t)
 a 1D Epanechnikov kernel function, e.g. for Kernel Density Estimation
 
double jkqtpstatKernel1DGaussian (double t)
 a 1D Gaussian kernel function, e.g. for Kernel Density Estimation
 
double jkqtpstatKernel1DPicard (double t)
 a 1D Picard kernel function, e.g. for Kernel Density Estimation
 
double jkqtpstatKernel1DQuartic (double t)
 a 1D quartic kernel function, e.g. for Kernel Density Estimation
 
double jkqtpstatKernel1DTriangle (double t)
 a 1D Epanechnikov kernel function, e.g. for Kernel Density Estimation
 
double jkqtpstatKernel1DTricube (double t)
 a 1D tricube kernel function, e.g. for Kernel Density Estimation
 
double jkqtpstatKernel1DTriweight (double t)
 a 1D triweight kernel function, e.g. for Kernel Density Estimation
 
double jkqtpstatKernel1DUniform (double t)
 a 1D uniform kernel function, e.g. for Kernel Density Estimation
 

Detailed Description

Function Documentation

◆ jkqtpstatKernel1DCauchy()

double jkqtpstatKernel1DCauchy ( double  t)
inline

a 1D Cauchy kernel function, e.g. for Kernel Density Estimation

\[ k(t):=\frac{1}{\pi(1+t^2)} \]

◆ jkqtpstatKernel1DCosine()

double jkqtpstatKernel1DCosine ( double  t)
inline

a 1D cosine kernel function, e.g. for Kernel Density Estimation

\[ k(t) :=\begin{cases}\frac{\pi}{4}\cos\left(\frac{\pi}{2}t\right), & \text{if }t\in [-1;1]\\0, & \text{else}\end{cases} \]

◆ jkqtpstatKernel1DEpanechnikov()

double jkqtpstatKernel1DEpanechnikov ( double  t)
inline

a 1D Epanechnikov kernel function, e.g. for Kernel Density Estimation

\[ k(t) :=\begin{cases}\frac{3}{4} ( 1- t^2 ), & \text{if }t\in [-1;1]\\0, & \text{else}\end{cases} \]

◆ jkqtpstatKernel1DGaussian()

double jkqtpstatKernel1DGaussian ( double  t)
inline

a 1D Gaussian kernel function, e.g. for Kernel Density Estimation

\[ k(t):=\frac{1}{\sqrt{2\pi}}\exp \left(-\frac{1}{2}t^2\right) \]

◆ jkqtpstatKernel1DPicard()

double jkqtpstatKernel1DPicard ( double  t)
inline

a 1D Picard kernel function, e.g. for Kernel Density Estimation

\[ k(t):=\frac{1}{2}\exp(-|t|) \]

◆ jkqtpstatKernel1DQuartic()

double jkqtpstatKernel1DQuartic ( double  t)
inline

a 1D quartic kernel function, e.g. for Kernel Density Estimation

\[ k(t) :=\begin{cases}\frac{15}{16}(1-t^2)^2, & \text{if }t\in [-1;1]\\0, & \text{else}\end{cases} \]

◆ jkqtpstatKernel1DTriangle()

double jkqtpstatKernel1DTriangle ( double  t)
inline

a 1D Epanechnikov kernel function, e.g. for Kernel Density Estimation

\[ k(t) :=\begin{cases}1-|t|, & \text{if }t\in [-1;1]\\0, & \text{else}\end{cases} \]

◆ jkqtpstatKernel1DTricube()

double jkqtpstatKernel1DTricube ( double  t)
inline

a 1D tricube kernel function, e.g. for Kernel Density Estimation

\[ k(t) :=\begin{cases}\frac{70}{81}(1-|t|^3)^3, & \text{if }t\in [-1;1]\\0, & \text{else}\end{cases} \]

◆ jkqtpstatKernel1DTriweight()

double jkqtpstatKernel1DTriweight ( double  t)
inline

a 1D triweight kernel function, e.g. for Kernel Density Estimation

\[ k(t) :=\begin{cases}\frac{35}{32}(1-t^2)^3, & \text{if }t\in [-1;1]\\0, & \text{else}\end{cases} \]

◆ jkqtpstatKernel1DUniform()

double jkqtpstatKernel1DUniform ( double  t)
inline

a 1D uniform kernel function, e.g. for Kernel Density Estimation

\[ k(t) :=\begin{cases}0.5, & \text{if }t\in [-1;1]\\0, & \text{else}\end{cases} \]