Functions for Statistical Distributions in R
R provides a comprehensive set of functions for working with statistical distributions. These functions allow you to compute densities, probabilities, quantiles, and generate random numbers from various distributions.
Normal Distributions
dnorm() Function
Returns the density of the normal distribution for a given value.
Example:
# Density of the normal distribution at x = 0 density <- dnorm(0) print(density) # [1] 0.3989423
pnorm() Function
Returns the cumulative distribution function (CDF) value for a given point.
Example:
# CDF value for x = 1 cdf <- pnorm(1) print(cdf) # [1] 0.8413447
qnorm() Function
Returns the quantile corresponding to a given probability.
Example:
# Quantile for a probability of 0.95 quantile <- qnorm(0.95) print(quantile) # [1] 1.644854
rnorm() Function
Generates random values from a normal distribution.
Example:
# Generate 5 random values with mean = 0 and standard deviation = 1 random_values <- rnorm(5) print(random_values) # [1] -0.9785523 1.0217856 0.0638721 -0.2428278 -0.5025177
Binomial and Bernoulli Distributions
dbinom() Function
Returns the probability of a specific number of successes in a binomial distribution.
Example:
# Probability of exactly 3 successes in 10 trials with a success probability of 0.5 prob <- dbinom(3, size = 10, prob = 0.5) print(prob) # [1] 0.1171875
pbinom() Function
Returns the cumulative distribution function (CDF) value for a binomial distribution.
Example:
# CDF value for up to 3 successes in 10 trials with a success probability of 0.5 cdf <- pbinom(3, size = 10, prob = 0.5) print(cdf) # [1] 0.2167969
qbinom() Function
Returns the quantile corresponding to a given probability in a binomial distribution.
Example:
# Quantile for a probability of 0.95 in a binomial distribution with 10 trials and success probability 0.5 quantile <- qbinom(0.95, size = 10, prob = 0.5) print(quantile) # [1] 8
rbinom() Function
Generates random values from a binomial distribution.
Example:
# Generate 5 random values from a binomial distribution with 10 trials and a success probability of 0.5 random_values <- rbinom(5, size = 10, prob = 0.5) print(random_values) # [1] 7 5 6 4 6
Poisson Distributions
dpois() Function
Returns the probability of a specific number of events in a Poisson distribution.
Example:
# Probability of exactly 3 events with a mean rate of 2 prob <- dpois(3, lambda = 2) print(prob) # [1] 0.180447
ppois() Function
Returns the cumulative distribution function (CDF) value for a Poisson distribution.
Example:
# CDF value for up to 3 events with a mean rate of 2 cdf <- ppois(3, lambda = 2) print(cdf) # [1] 0.815263
qpois() Function
Returns the quantile corresponding to a given probability in a Poisson distribution.
Example:
# Quantile for a probability of 0.95 with a mean rate of 2 quantile <- qpois(0.95, lambda = 2) print(quantile) # [1] 4
rpois() Function
Generates random values from a Poisson distribution.
Example:
# Generate 5 random values with a mean rate of 2 random_values <- rpois(5, lambda = 2) print(random_values) # [1] 1 2 4 1 3
Exponential Distributions
dexp() Function
Returns the density of the exponential distribution for a given value.
Example:
# Density of the exponential distribution at x = 1 with rate = 1 density <- dexp(1, rate = 1) print(density) # [1] 0.3678794
pexp() Function
Returns the cumulative distribution function (CDF) value for an exponential distribution.
Example:
# CDF value for x = 1 with rate = 1 cdf <- pexp(1, rate = 1) print(cdf) # [1] 0.6321206
qexp() Function
Returns the quantile corresponding to a given probability in an exponential distribution.
Example:
# Quantile for a probability of 0.95 with rate = 1 quantile <- qexp(0.95, rate = 1) print(quantile) # [1] 2.995732
rexp() Function
Generates random values from an exponential distribution.
Example:
# Generate 5 random values with rate = 1 random_values <- rexp(5, rate = 1) print(random_values) # [1] 0.4161032 0.2125973 0.5747574 1.2425372 0.3794684
Chi-Square Distributions
dchisq() Function
Returns the density of the chi-square distribution for a given value.
Example:
# Density of the chi-square distribution at x = 5 with 2 degrees of freedom density <- dchisq(5, df = 2) print(density) # [1] 0.2650259
pchisq() Function
Returns the cumulative distribution function (CDF) value for a chi-square distribution.
Example:
# CDF value for x = 5 with 2 degrees of freedom cdf <- pchisq(5, df = 2) print(cdf) # [1] 0.878813
qchisq() Function
Returns the quantile corresponding to a given probability in a chi-square distribution.
Example:
# Quantile for a probability of 0.95 with 2 degrees of freedom quantile <- qchisq(0.95, df = 2) print(quantile) # [1] 7.378699
rchisq() Function
Generates random values from a chi-square distribution.
Exemple :
# Generate 5 random values with 2 degrees of freedom random_values <- rchisq(5, df = 2) print(random_values) # [1] 1.326664 3.046862 1.685939 3.128086 2.093674
Summary
- Normal Distributions: dnorm(), pnorm(), qnorm(), rnorm()
- Binomial Distributions: dbinom(), pbinom(), qbinom(), rbinom()
- Poisson Distributions: dpois(), ppois(), qpois(), rpois()
- Exponential Distributions: dexp(), pexp(), qexp(), rexp()
- Chi-Square Distributions: dchisq(), pchisq(), qchisq(), rchisq()