The normal distribution function in R

Norm indicates a normal distribution:

rnorm (x): indicates the generation of a random x normal distribution sequence, random

dnorm (x): the probability density functionof the output normal distribution, density function ———— plot (dnorm (x)), to draw the density curve

pnorm (x): distribution function for output normal distribution , probability function,probability functions

"For continuous distribution, the distribution function is the result of integrals from negative infinity to X to the probability density function"

Qnorm (p): the quantile function,fuction. Given a probability p, the function returns an x indicating the x value when the probability is p.

[ The distribution function of the continuous random variable X is f (x), and the density function is P (x). So, p for any 0<p<1, called F (x) =p x for this distribution of the division number, or the lower side of the sub-position. To put it simply, a sub-number refers to a point in a continuous distribution function, which corresponds to the probability p. ]

Help (Dnorm):

dnorm gives the density, pnorm gives the distribution function, qnorm gives the quantile functi on[), and rnorm generates random deviates.

Dnorm (x, mean = 0, SD = 1, log = FALSE) is the standard normal distribution by default
Pnorm (q, mean = 0, SD = 1, Lower.tail = TRUE, LOG.P = FALSE)
Qnorm (p, mean = 0, SD = 1, Lower.tail = TRUE, LOG.P = FALSE)
Rnorm (n, mean = 0, SD = 1)

X, Q:vector of Quantiles. The number of bits of a vector

P:vector of probabilities. Vector probability

N:number of observations. If length (n) > 1, the length is taken to be the number required.

Mean:vector of means.

Sd:vector of standard deviations.

Log, log.p:logical; If TRUE, probabilities p is given as log (P).

If log.p=true, it is calculated as Qnrom (log (p)) when computed with Qnorm (p). " due to the probability of P-0~1, when this range is exceeded, this method is equivalent to an enlarged calculation range." such as Qnorm (-.5,log.p=f) = = Qnorm (log (-.5), log.p=f), later verified that this understanding is wrong , what is correct? "

lower.tail:logical; If TRUE (default), probabilities is p[x≤x] Otherwise, p[x > X].

If lower.tail=true, the probability of the left area is computed, i.e. p[x≤x]; otherwise right p[x > x]=1-p[x≤x]

Normal distribution function:

, in this formula when μ=0, σ=1,

The standard normal distribution functions are:

A few interesting examples of easy to understand formulas:

Dnorm (0) = = 1/sqrt (2*PI), at this time x=0,μ=0,σ=1
Dnorm (1) = = exp ( -1/2)/sqrt (2*PI), the equivalent of the following formula
Dnorm (1) = = 1/sqrt (2*pi*exp (1)), at this time x=1,μ=0,σ=1

For the addition of the number of bits:

The Division function: The division function is the inverse function of the cumulative distribution function "Probability function", that is to say, given the probability value, the value of the random variable (left-hand division) is computed.

There are four distributions that are commonly used for the number of bits:

Standard normal distribution, Qnorm (p, mean=0, sd=1)

Student ' s (t), QT (p,df=n,ncp=0)

Chi-Square Distribution: QCHISQ (p, df=n,ncp=0)

FISHER-SNEDECOR:QF (p, df1,df2,ncp=0)

Exception:

Quartile: Four the number of points in the Statistical Division is one of the statistics, that is, all the values from small to large and divided into four equal parts, in three points is four.

The normal distribution function in R