`R/poly_orthonormal_basis.R`

`poly_orthonormal_basis.Rd`

Build an orthonormal basis, needed to decompose the probability density function (pdf) of the unknown component from the admixture, depending on the support under consideration.

poly_orthonormal_basis( support = c("Real", "Integer", "Positive", "Bounded.continuous", "Bounded.discrete"), deg, x, m )

support | Support of the random variables implied in the two-component mixture distribution. |
---|---|

deg | Degree up to which the basis is built. |

x | (NULL by default) Only used when support is 'Integer'. The point at which the polynomial value will be evaluated. |

m | (NULL by default) Only used when support is 'Integer'. Corresponds to the mean of the reference measure, i.e. Poisson(m). |

the orthonormal polynomial basis used to decompose the density of the unknown component of the mixture distribution.

Xavier Milhaud xavier.milhaud.research@gmail.com

poly_orthonormal_basis(support = 'Real', deg = 10, x = NULL, m = NULL)#> [[1]] #> 1 #> #> [[2]] #> x #> #> [[3]] #> -1 + x^2 #> #> [[4]] #> -3*x + x^3 #> #> [[5]] #> 3 - 6*x^2 + x^4 #> #> [[6]] #> 15*x - 10*x^3 + x^5 #> #> [[7]] #> -15 + 45*x^2 - 15*x^4 + x^6 #> #> [[8]] #> -105*x + 105*x^3 - 21*x^5 + x^7 #> #> [[9]] #> 105 - 420*x^2 + 210*x^4 - 28*x^6 + x^8 #> #> [[10]] #> 945*x - 1260*x^3 + 378*x^5 - 36*x^7 + x^9 #> #> [[11]] #> -945 + 4725*x^2 - 3150*x^4 + 630*x^6 - 45*x^8 + x^10 #>