# Weibull Distribution in R

Weibull Distribution in R, Weibull Distribution was discovered by Swedish physicist Wallodi Weibull in 1939.

A continuous random variable X is said to follow Weibull distribution if its probability density function

fx(x; α, β)= α/βα [x α-1e(-x/ β)^α]

For x>0, α, β>0.

There are two parameters in this distribution and It can be used in reliability theory. Corrosion, alloy weight loss, and metal tensile strength all follow the Weibull distribution.

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## Weibull Distribution in R

Let’s see how to plot Weibull distribution in R.

Syntax:-

```dweibull(x, shape, scale = 1) to create the probability density function.
curve(function, from = NULL, to = NULL) to plot the probability density function.```

Weibull distribution based on parameters shape = 2 and scale = 2 where the x-axis of the plot ranges from 0 to 5:

A specific instance of the generalized gamma distribution is the Weibull distribution.

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`curve(dweibull(x, shape=2, scale = 2), from=0, to=5)` Let’s make it aesthetically appealing better,

```curve(dweibull(x, shape=2, scale = 2), from=0, to=5,
main = 'Weibull Distribution (shape = 2, scale = 2)',
ylab = ' dWeibull gives the density',
lwd = 2,
col = 'pink')``` Let’s see how to add more than one curve in the same plot

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```curve(dweibull(x, shape=2, scale = 2), from=0, to=5,
main = 'Weibull Distribution',
ylab = ' dWeibull gives the density',
lwd = 2,
col = 'pink')```
`curve(dweibull(x, shape=1.5, scale = 2), from=0, to=5, col='green', add=TRUE)` We can add a legend to the plot by using the legend() function,

```legend(2, .3, legend=c("shape=2, scale=2", "shape=1.5, scale=2"),
col=c("green", "blue"), lty=1, cex=1.2)```  