NCL Home > Documentation > Functions > Statistics, Bootstrap


Extract the user specified element from the bootstrapped values.

Available in version 6.4.0 and later.


load "$NCARG_ROOT/lib/ncarg/nclscripts/csm/bootstrap.ncl"

	function bootstrap_estimate (
		xBoot   : numeric,          
		fpc [1] : float or double,  
		opt [1] : logical           

	return_val [ numeric value or array  ] 



An array containing the bootstrapped values in ascending order as returned by the bootstrap_* functions.


A scalar between 0 and 1 (0.0 < fpc < 1.0) which specifies the desired level.


Currently not used. Set to False.

Return value

All appropriate meta data are returned. Please use printVarSummary(...) to examine the returned variable.


A simple function that calculates the appropriate index value corresponding to the fraction fpc and extracts that value or array from the xBoot array. All appropriate meta data are returned.


Computer Intensive Methods in Statistics 
   P. Diaconis and B. Efron 
   Scientific American (1983), 248:116-130  
An Introduction to the Bootstrap 
   B. Efron and R.J. Tibshirani, Chapman and Hall (1993) 
Bootstrap Methods and Permutation Tests: Companion Chapter 18 to the Practice of Business Statistics
   Hesterberg, T. et al (2003)

Climate Time Series Analysis: Classical Statistical and Bootstrap Methods
   M. Mudelsee (2014) Second edition. Springer, Cham Heidelberg New York Dordrecht London
   ISBN: 978-3-319-04449-1, e-ISBN: 978-3-319-04450-7
   doi: 10.1007/978-3-319-04450-7
   xxxii + 454 pp; Atmospheric and Oceanographic Sciences Library, Vol. 51

See Also

generate_sample_indices, bootstrap_stat, bootstrap_diff, bootstrap_correl, bootstrap_regcoef


Please see the Bootstrap and Resampling application page.

Example 1: Let x(N); y(N), N=100:

   nBoot       = 1000         ; user set
   nDim        = 0            ; or (/0,0/); dimension numbers corresponding to 'N'
   opt         = False        ; use all default options

   BootStrap   = bootstrap_correl(x, y, nBoot, nDim, opt)
   rBoot       = BootStrap[0] ; bootstrapped cross-correlations in ascending order
   rBootAvg    = BootStrap[1] ; Average of the bootstrapped cross correlations
   rBootStd    = BootStrap[2] ; Bootstrapped standard deviations
   delete(BootStrap)          ; no longer needed

   rBootLow    = bootstrap_estimate(rBoot, 0.025, False)   ;  2.5% lower confidence bound 
   rBootMed    = bootstrap_estimate(rBoot, 0.500, False)   ; 50.0% median of bootstrapped estimates
   rBootHi     = bootstrap_estimate(rBoot, 0.975, False)   ; 97.5% upper confidence bound

   printVarSummary(rBoot)    ; information only