Hi Uzzal,

kriging is usually used for the interpolation of spatial phenomena and it does not matter whether they are geological, physical, chemical or socio-economic, and it is believed that most of these phenomena do have a normal distribution. Moreover, kriging is driven by Gaussian process and estimate the mean value of the phenomenon meaning that normal distribution is quite essential. Although normality of data is often mentioned in the literature, you can use kriging also for the data in non-normal distribution in case you choose an appropriate method. However, it is ideal when data follows normality at least approximately or it is possible to transform them because then kriging provides the best estimates and it is possible to create confidence intervals.

In case that you are beginning with geostatistical analyses, I would recommend you some of the publications that are linked below. I am also sure that you can find a plethora of another free sources through the web.

Regards

Lukas

http://spatial-analyst.net/book/system/files/Hengl_2009_GEOSTATe2c1w.pdf

http://eusoils.jrc.ec.europa.eu/ESDB_Archive/eusoils_docs/other/EUR22904en.pdf

http://www.springer.com/us/book/9781461476177

This question has been answered elsewhere on Researchgate.net but it seems to re-appear from time to time. The derivation of the kriging equations (to determine the coefficients in the kriging estimator (whether Simple kriging, Ordinary krigng, Universal kriging, Indicator kriging, Cokriging, etc) does not depend on any distribution assumptions. It is not true that " kriging is driven by Gaussian process and estimate the mean value of the phenomenon meaning that normal distribution is quite essential". It is true that if the random function (not the data) is multivariate Gaussian then the Simple kriging estimator is the same as the conditional expectation (which is the optimal unbiased estimator). It is true that some of G. Matheron's work was motivated by this coincidence. It is also true that if the empirical distribution of the data is skewed then the kriging estimators are sensitive to a few large data vaues but normality is not a requirement for kriging. If a transformation is used then it should be a multivariate transformation. As for references, it would be better to look at Matheron's  1973 paper in Advances in applied Probability or the volume by Chiles and Delfiner (J. Wiey & Sons, there are two editions).titled "Geostatistics"

There is a Bayesian approach to kriging which is based on normality (see the book "Model Based Geostatistics"  Springer).

The key assumption is the right form of stationarity (second order, intrinsic), not the probability distribution

The distributional assumptions are with respect to the "residuals" of the model, but the not necessarily the data itself. There are many kriging methods, some are based on linear models, i.e. simple & ordinary & universal kriging. For linear modeling approaches the distributional or Gaussian assumption is not required.But yo get skrewed results when the distribution is not symmetric. Furthermore, if you like to perform tests and construct confidence or prediction intervals, then you need a distribution to base these on.

I hope this helps, Olaf

Simple, Ordinary and Universal kriging are not based on linear models and there are no "residuals"

Hi,

You can apply simple, ordinary,... kriging method for data regardless of their distribution. It provides estimation for the unsampled location/time. But note that the distribution of the estimated values will be Gaussian, especially if the number of samples is large. That is because of the fact that the estimation for each unsampled location/time is a linear combination of sampled ones, and according to central limit theorem, it will be normally distributed, regardless of the distribution of data.

So, if it is ok to have a normally distributed output, no transformation will be required. 

Please correct me, if I'm wrong. 

Regards,

Mohammad

The CLT is based on several assumptions and they are unlikely to be satisfied. The simplest version of the CLT pertains to a sequence of independent random variables, identically distributed with the same variance. The convergence is "in distribution" which is a weak form of convergence. Sorry but your conclusion is not justified

Hi Uzzal Dash

Normality of the sample data distribution is known to improve the results from kriging. Transformation is very important to make the data more symmetrical, linear and constant in variance. Data were accepted as normally distributed if the computed Kolmogorov-Smirnov statistic (Dmax) was less than the corresponding critical value for the 5% level of significance .

Y

Your answer is completely wrong, everything you said is wrong.

The original question is wrong and implies a complete misunderstanding of kriging