# Weibull distribution

This tool is really simple to use and this tool is free and web based tool that will help you a lot.

#### Input

$$\normalsize\ percentile\ x (x≧0)= 1$$ $$\normalsize\ shape\ parameter\ a (a＞0)= 2$$ $$\normalsize\ scale\ parameter\ b(b＞0)= 1$$

#### Solution

$$probability\ density\ f\ =0.7357588823428846431911$$ $$lower\ cumulative\ P\ =0.6321205588285576784045$$

#### Formula

$$\normalsize Weibull\ distribution$$ $$(1)\ probability\ density\\ \hspace{30px}f(x,a,b)={\large\frac{a}{b}(\frac{x}{b})^{a-1}e^{-(\frac{x}{b})^a}}$$ $$(2)\ lower\ cumulative\ distribution$$ $$\hspace{30px}P(x,a,b)={\large\int_{\small 0}^{\small x}}f(t,a,b)dt={\large 1-e^{-(\frac{x}{b})^a}}$$

# What is Weibull Distribution?

The Wei-bull Distribution is a persistent likelihood appropriation named after Swedish mathematician Waloddi Wei-bull. He initially proposed the dispersion as a model for material breaking strength, however perceived the capability of the circulation in his 1951 paper A Statistical Distribution Function of Wide Applicability. Today, it's generally used to survey item unwavering quality, investigate life information, and model failure times. The Wei-bull can likewise fit a wide scope of information from numerous different fields, including science, financial aspects, designing sciences, and hydrology (Rinne, 2008).

In spite of the fact that it's incredibly valuable as a rule, the Wei-bull is definitely not a suitable model for each circumstance. For instance, compound responses and erosion Distribution are generally demonstrated with the log-normal conveyance.

## Observation of the weibull Distribution

In the event that x speaks to "time-to-disappointment", the Weibull dispersion is portrayed by the way that the disappointment rate is corresponding to an intensity of time, specifically β – 1. Accordingly β can be deciphered as follows:

• An estimation of β < 1 shows that the disappointment rate diminishes over the long run. This occurs if there is critical "newborn child mortality", or where inadequate things bomb ahead of schedule with a disappointment rate diminishing over the long haul as the faulty things are removed of the populace.
• An estimation of β = 1 demonstrates that the disappointment rate is consistent after some time. This may propose arbitrary outer occasions are causing mortality or failure.
• An estimation of β > 1 shows that the disappointment rate increments with time. This occurs if there is an "maturing" measure; for example on the off chance that parts are bound to wear out as well as come up short over the long haul.
• 1/α can be seen as the failure rate. The mean of the Wei-bull distribution is the interim to failure (MTTF) or interim between disappointments (MTBF) = \alpha \Gamma \! \left( \! 1+\frac{1}{\beta} \! \right).

### How to use this tool Weibull Distribution calculator?

This tool is really simple to use and this tool is free and web-based tool that will help you a lot. This tool will give you really a very quick solution just in a second so so you don”t have to waste time doing manually. You can solve all the problems related to the Weibull  Distribution.

To use this tool you just have to follow some really simple steps that will help you a lot because this tool is not that much hard to use.

So as you are in this page already so that you will see some of the boxes here where you will enter the value here.

After you will enter all the values in the text boxes you should cross-check it once again.

After that you just have to simply click on the calculate button to get the answer of your equation.

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