# EffectiveRange: Effective range for some spatial correlation functions In StempCens: Spatio-Temporal Estimation and Prediction for Censored/Missing Responses

## Description

It computes the effective range for an isotropic spatial correlation function, which is commonly defined to be the distance from which the correlation becomes small, typically below 0.05.

## Usage

 `1` ```EffectiveRange(cor = 0.05, phi, kappa = 0, Sp.model = "exponential") ```

## Arguments

 `cor` effective correlation to check for. By default = 0.05. `phi` spatial scaling parameter. `kappa` smoothness parameter, required by the matern and power exponential functions. By default = 0. `Sp.model` type of spatial correlation function: '`exponential`' for exponential, '`gaussian`' for gaussian, '`matern`' for matern, '`pow.exp`' for power exponential and '`spherical`' for spherical function, respectively. By default = `exponential`.

## Details

The available isotropic spatial correlation functions are:

Exponential:

Corr(d) = exp{-d/φ},

Gaussian:

Corr(d) = exp{-(d/φ)^2},

Matern:

Corr(d) = 1/(2^(κ-1)Γ(κ))(d/φ)^κ K_κ(d/φ),

Power exponential:

Corr(d) = exp{-(d/φ)^κ},

Spherical:

Corr(d) = 1 - 1.5 d/φ + 0.5(d/φ)^3,

where d is the Euclidean distance between two observations, φ is the spatial scaling parameter, Γ(.) is the gamma function, κ is the smoothness parameter and K_κ(.) is the modified Bessel function of the second kind of order κ.

## Value

The function returns the effective range, i.e., the approximate distance from which the spatial correlation is lower than `cor`.

## Author(s)

Katherine L. Valeriano, Victor H. Lachos and Larissa A. Matos

## Examples

 ```1 2 3 4``` ```phi <- 164.60 range1 <- EffectiveRange(0.05, phi, kappa=0, Sp.model="exponential") range2 <- EffectiveRange(0.05, phi, kappa=1, Sp.model="pow.exp") # Note that these functions are equivalent. ```

### Example output

```
```

StempCens documentation built on Oct. 23, 2020, 7:28 p.m.