Continuous Distribution

Continuous distribution is a distribution of random variables which may assume any value in the number line whether integer or not. It is also known as continuous probability distributions and applied in six sigma to evaluate the processes in an improved manner. It is applied when the characteristic being examined are found to be a continuous variable.

Continuous distribution also known as continuous probability distributions play an important function in six sigma. The continuous distributions are used or applied when the characteristic being examined is a continuous variable, for instance weight, length etc. Continuous variable or continuous data are type of data that can be measured on a measurement scale and can be subdivided in precise and smaller measurements or recording system.

There are nine continuous distributions and below is a short introduction to all:

• Bimodal Distribution: It is a sort of continuous distribution and has two peaks. It usually comes about when the output from two process streams are mixed or blended. Each individual process stream conforms to a normal distribution but has a different standard deviation and mean.
• Bivariate Distribution: It confirms the joint probability distribution between or both two random variables. For instance, the position of the centre of a hole can differ in both ‘x’ and ‘y’ directions. The distribution of the centre position in ‘x’ and ‘y’ directions conform to a normal distribution. The bivariate probability distribution would be three dimensional surface and will be displaying the probability of the centre of a hole being in any position in the x-y plane. The surface permits you to solve the problems by calculating the probability of a hole centre being one standard deviation in ‘x’ and 2 standard deviations in ‘y’ from the mean position.
• Chi-Square Distribution: It is one of the vital distributions and is a continuous probability distribution with the probability density function.
• Exponential Distribution: It is a continuous probability distribution and can be represented by It is related to the Poisson distribution and used for reliability engineering. It acts as a useful phase as it models situation where the probability of failure rate is constant.
• F Distribution: It is a vital continuous probability distribution and formed from the rations of two chi-squared variables.
• Lognormal Distribution: It is also a continuous distribution with the probability distribution function.
• Normal Distribution: Also known as Gaussian distribution, they are in control and conform to a normal distribution. Furthermore, it is also a condition of many statistical tests.
• T Distribution: It has the probability function and the shape of the distribution is identical to the normal distribution. It also converges on the normal distribution as the number of degrees of freedom increases.
• Weibull Distribution: It is very flexible and used extensively in reliability engineering because the parameters can be formulated to suit the product characteristics specifically in the wear out phases and mortality of the life cycle.

In business operations, most experiments have sample spaces and may not contain finite number of simple events. A distribution is considered to be continuous if it is built on continuous random variables that are also variables which have the capability to assume the infinite values equivalent to points on a line interval. The vitality continuous distributions applied and used in business operations are the Lognormal, Normal, the Lognormal, the Exponential and the Weibull distributions.

In probability statistics and theory, a continuous probability distribution identifies either the probability of the value falling within a particular interval or probability of each value of an unknown random variable. The probability distribution illustrates the range of probable values that a random variable can achieve and the probability that the value of the random variable is within any measurable range.

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