# fRen: Sample Renyi function In rcosmo: Cosmic Microwave Background Data Analysis

## Description

This function computes values of the sample Renyi function. Returns the estimated values of T(q) for q taking values on a grid. For large data sets could be rather time consuming.

## Usage

 ```1 2``` ```fRen(cmbdf, q.min = 1.01, q.max = 10, N = 20, k.box = log2(nside(cmbdf)) - 3, intensities = "I") ```

## Arguments

 `cmbdf` A `CMBDataFrame`. `q.min` Left endpoint of the interval to compute the Renyi function. The default value is 1.01, `q.max` Right endpoint of the interval to compute the Renyi function. The default value is 10 `N` Number of points to compute the Renyi function. The default value is 20. `k.box` A dyadic decomposition level in computing the Renyi function, see the references in Details. The default value is log2(nside(cmbdf)) - 3 `intensities` A CMBDataFrame column with measured values

## Value

Data frame which first column is the sampling grid seq(q.min, q.max, length.out = N) of q values. Another column consists of values of the sample Renyi function T(q) computed on the grid using the k.boxth level dyadic decomposition of the unit ball.

## References

(1) Leonenko, N., and Shieh, N. 2013. Rényi function for multifractal random fields. Fractals 21, Article No. 1350009.

(2) http://mathworld.wolfram.com/RenyiEntropy.html

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```## Download the map first # downloadCMBMap(foreground = "smica", nside = 1024) # # cmbdf <- CMBDataFrame("CMB_map_smica1024.fits") # win <- CMBWindow(theta = c(pi/4,pi/2,pi/2), phi = c(0,0,pi/2)) # cmbdf<- window(cmbdf, new.window = win) # Tq <- fRen(cmbdf) # # plot(Tq[,1], Tq[,2], ylab =expression(D[q]), xlab = "q", # main = "Sample Renyi function", pch = 20, col = "blue") ```

rcosmo documentation built on Feb. 14, 2020, 5:06 p.m.