Can lognormal distribution give negative mean for hydraulic conductivity for clayey soil?

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Subrata Chakraborty

@Santosh

Ks is lognormally distributed. Then mean can not be negative. Have you fitted lognormal distribution to Ks? what is the pdf? What are the estimated parameters? If you share the detail may be I can see. Best.

Richard David Gill

This is a question about statistics, not about probability. And you need to do statistics with decent, modern, professional, tools. You need R, not Excel.

The two-parameter log normal distribution is the distribution of the exponent of a normally distributed random variable. The outcomes vary between 0 and infinity.

Some people allow also shifts of the whole distribution. We then get the three-parameter lognormal. Ie the distribution of c + the exponent of N(mu, sigma^2), parameters c, mu, sigma. The outcomes vary between c and infinity.

Girish Kumar

Yes, it is possible to have a negative value for lognormal mean. The main purpose of using a lognormal distribution for probabilistic analysis is to have only positive values assigned to the variables (engineering properties like hydraulic conductivity). The lognormal of the variables is normally distributed however, you would be interested in assigning the corresponding normally distributed value to the hydraulic conductivity, and in that case you will happen to raise the lognormal mean to the exponent function rendering positive values only (exponent function is always positive). Hope this helps.