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
)

## Arguments

support Support of the random variables implied in the two-component mixture distribution. Degree up to which the basis is built. (NULL by default) Only used when support is 'Integer'. The point at which the polynomial value will be evaluated. (NULL by default) Only used when support is 'Integer'. Corresponds to the mean of the reference measure, i.e. Poisson(m).

## Value

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

## Author

Xavier Milhaud xavier.milhaud.research@gmail.com

## Examples

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
#>