R Normal Distribution - r - learn r - r programming
- In a random collection of data from independent sources, it is generally observed that the distribution of data is normal.
- Which means, on plotting a graph with the value of the variable in the horizontal axis and the count of the values in the vertical axis we get a bell shape curve.
- The center of the curve represents the mean of the data set.
- In the graph, fifty percent of values lie to the left of the mean and the other fifty percent lie to the right of the graph.
- This is referred as normal distribution in statistics.
- R has four in built functions to generate normal distribution.
r programming normal distribution
dnorm(x, mean, sd)
pnorm(x, mean, sd)
qnorm(p, mean, sd)
rnorm(n, mean, sd)
- Following is the description of the parameters used in above functions −
- x is a vector of numbers.
- p is a vector of probabilities.
- n is number of observations (sample size).
- mean is the mean value of the sample data. It's default value is zero.
- sd is the standard deviation. It's default value is 1.
dnorm()
- This function gives height of the probability distribution at each point for a given mean and standard deviation.
# Create a sequence of numbers between -10 and 10 incrementing by 0.1.
x <- seq(-10, 10, by = .1)
# Choose the mean as 2.5 and standard deviation as 0.5.
y <- dnorm(x, mean = 2.5, sd = 0.5)
# Give the chart file a name.
png(file = "dnorm.png")
plot(x,y)
# Save the file.
dev.off()
- When we execute the above code, it produces the following result −
pnorm()
- This function gives the probability of a normally distributed random number to be less that the value of a given number.
- It is also called "Cumulative Distribution Function".
# Create a sequence of numbers between -10 and 10 incrementing by 0.2.
x <- seq(-10,10,by = .2)
# Choose the mean as 2.5 and standard deviation as 2.
y <- pnorm(x, mean = 2.5, sd = 2)
# Give the chart file a name.
png(file = "pnorm.png")
# Plot the graph.
plot(x,y)
# Save the file.
dev.off()
- When we execute the above code, it produces the following result −
qnorm()
- This function takes the probability value and gives a number whose cumulative value matches the probability value.
# Create a sequence of probability values incrementing by 0.02.
x <- seq(0, 1, by = 0.02)
# Choose the mean as 2 and standard deviation as 3.
y <- qnorm(x, mean = 2, sd = 1)
# Give the chart file a name.
png(file = "qnorm.png")
# Plot the graph.
plot(x,y)
# Save the file.
dev.off()
- When we execute the above code, it produces the following result −
rnorm()
- This function is used to generate random numbers whose distribution is normal. It takes the sample size as input and generates that many random numbers. We draw a histogram to show the distribution of the generated numbers.
# Create a sample of 50 numbers which are normally distributed.
y <- rnorm(50)
# Give the chart file a name.
png(file = "rnorm.png")
# Plot the histogram for this sample.
hist(y, main = "Normal DIstribution")
# Save the file.
dev.off()
