3.5.3.2.8 Ks2densityks2density-func
Definition:
z = ks2density(x, y, vX, vY, wx, wy) returns the 2D kernel density at point (x, y) with respect
to a function established by datasets (vX, vY) with scale (wx, wy), where scale (wx, wy) are determined by estimation function Kernel2width.
/math-310345fbaf2b947f7ef2b28e31540a48.png?v=0 "\text{ks2density}(x,y,\text{vX},\text{vY},w_x,w_y) = \frac{1}{n} \sum_{i=1}^{n} \frac{1}{ 2\pi w_x w_y } \exp \left(-\frac{(x-\text{vX}_i)^2}{2w_x ^2} - \frac{(y-\text{vY}_i)^2}{2w_y^2} \right)")
where n is the number of elements in vector vX or vY, /math-d42590de7df507482af1323d9ced6ebd.png?v=0 "\text{vX}_i") is ith element in vector vX and /math-cc693045aa2161426c9f2b97f77a6a49.png?v=0 "\text{vY}_i") is ith element in vector vY.
Parameters:
/math-9dd4e461268c8034f5c8564e155c67a6.png?v=0 "x") (input, double)- x value to evaluate for 2D kernel density
/math-415290769594460e2e485922904f345d.png?v=0 "y") (input, double)- y value to evaluate for 2D kernel density
/math-dc072f8459258f6cfa11f1d4178e8ffc.png?v=0 "\text{vX}") (input, vector)- x values of distributed samples used as kernel centers
/math-bc9ba356dae056089eb9b2ba5ea6785f.png?v=0 "\text{vY}") (input, vector)- y values of distributed samples used as kernel centers
/math-4a5d1969fe1ef947082a32d547c247d7.png?v=0 "w_x") (input, double)- The bandwidth of X scale,
/math-4dd5f9a976d0e27c4c9f2ed04a9c2558.png?v=0 "w_x > 0")
/math-e939f0323d8d49a8482b30a5284c8374.png?v=0 "w_y") (input, double)- The bandwidth of Y scale,
/math-6f306a2665477247b1b171b197840b6b.png?v=0 "w_y > 0")
/math-fbade9e36a3f36d3d676c1b808451dd7.png?v=0 "z") (output, double)- 2D kernel density at point
/math-90cbc22edf225adf8a68974f51227f05.png?v=0 "(x,y)") with respect to a function established by datasets (vX,vY) with scale /math-3b50d54d0e3073eed2cff0f4c00763f9.png?v=0 "(w_x,w_y)")
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