On 07-Sep-09 06:42:06, Gundala Viswanath wrote: > How do people usually use the result of density function (e.g. dnorm)? > Especially when its value can be greater than 1. > > What do they do with such density >1? > >> dnorm(2.02,2,.24) > [1] 1.656498 > > - G.V.
The point is that it is a *density* of probability. The greater the density, the more compactly a given amount of probability is distributed over a given range of X (or, the narrower the range of X ove which a given amount of probability is distributed); the lower the density, the more widely it is dispersed. The concept of density is, in effect, the amount of probability per unit length in an interval, so "division by length" is part of it. To convert probability density to probability, multiply by a length. To obtain (a close approximation to) the amount of probability within a short range, such as 2.01 to 2.03, when X has your Normal distribution with mean 2.02 and SD 0.24, multiply the value of the density function at the midpoint 2.02 by the length 0.02 of the interval: dnorm(2.02,2,.24)*0.02 # = 0.03312996 and compare it with the amount of probability calculated from pnorm: pnorm(2.03,2,.24) - pnorm(2.01,2,.24) # = 0.03312044 The approximation is even closer for shorter intervals. Consider the ratio between the approximate and the true probabilities for an interval of length 0.0002: (dnorm(2.02,2,.24)*0.0002)/(pnorm(2.0201,2,.24) - pnorm(2.0199,2,.24)) # = 1 In fact, 1 - (dnorm(2.02,2,.24)*0.0002)/ (pnorm(2.0201,2,.24) - pnorm(2.0199,2,.24)) # = -2.873419e-08 Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <ted.hard...@manchester.ac.uk> Fax-to-email: +44 (0)870 094 0861 Date: 07-Sep-09 Time: 10:14:00 ------------------------------ XFMail ------------------------------ ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.