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Two functions for normal distributions

Function inorm

X ~ N (mean = 15, sd = 5)

You want to know the interval in which a certain percentage (suppose the 80 %) of X values varies.

The following function solves this kind of problem.

inorm <- function(p, mean = 0, sd = 1) {

    if (p <= 0 | p >= 1) 
        stop("The interval makes sense with a probability greater than 0 and lower than 1")

    LL <- qnorm((1 - p)/2, mean, sd)

    UL <- 2 * mean - LL

    interv <- c(LL, UL)
    names(interv) <- c("Lower Limit", "Upper Limit")

    return(interv)
}

So, if you apply the function to this special case:

inorm(0.8, 15, 5)

## Lower Limit Upper Limit 
##       8.592      21.408

Function prmtnorm

You have 2 quantiles of a normal distribution and the probability associated to (lower than) each of them.

You want to know the parameters of this distribution, so you are looking for mean and standard deviation.

prmtnorm <- function(quantile1, p1, quantile2, p2) {

    if (p1 <= 0 | p2 <= 0 | p1 >= 1 | p2 >= 1) 
        stop("Both p1 and p2 must belong to ]0,1[")

    sdev <- (quantile1 - quantile2)/(qnorm(p1) - qnorm(p2))

    if (sdev <= 0) 
        stop("Wrong input")

    MEAN <- quantile1 - sdev * qnorm(p1)

    output <- c(MEAN, sdev)
    names(output) <- c("mean", "sd")

    return(output)
}

Example:

If you know that, in a small town, the size of the 10 % of houses is lower than 150 m2 and the size of the 30 % of houses is higher than 250 m2, you can easily obtain mean and standard deviation, assuming you are dealing with a normal distribution.

prmtnorm(quantile1 = 150, p1 = 0.1, quantile2 = 250, p2 = 1 - 0.3)

##   mean     sd 
 ## 220.96  55.37
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