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$$\normalsize\ percentile\ x (x≧0)= 1$$ $$\normalsize\ shape\ parameter\ a (a＞0)= 2$$ $$\normalsize\ scale\ parameter\ b(b＞0)= 1$$
$$probability\ density\ f\ =0.7357588823428846431911$$ $$lower\ cumulative\ P\ =0.6321205588285576784045$$
$$\normalsize Weibull\ distribution$$ $$(1)\ probability\ density\\ \hspace{30px}f(x,a,b)={\large\frac{a}{b}(\frac{x}{b})^{a-1}e^{-(\frac{x}{b})^a}}$$ $$(2)\ lower\ cumulative\ distribution$$ $$ \hspace{30px}P(x,a,b)={\large\int_{\small 0}^{\small x}}f(t,a,b)dt={\large 1-e^{-(\frac{x}{b})^a}}$$
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.
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:
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