1 / 23

presetation on uniform distribution

presentation on uniform distribution with its properties

humna15
Download Presentation

presetation on uniform distribution

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Uniform Distribution

  2. Presented by • HUMNA ZAHID 236-FBAS/BSST F-17 • NAYYAB SHAHID 237-FBAS/ BSST F-17 • AFSHEEN 232-FBAS/ BSST F-17 • SHAFAQ GULZAR 219-FBAS/ BSST F-17 • TAYYAB NORIEN 215-FBAS/ BSST F-17

  3. Background of Uniform Distribution "Uniform distribution appears in 1937 in Introduction to Mathematical Probability by J. V. Uspensky, "A stochastic variable is said to have uniform distribution of probability if probabilities attached to two equal intervals are equal." This is a slight variant of the modern terminology, which would be "a variable is said to be uniformly distributed" or "a variable from the uniform distribution". Uniformly distributed is found in H. Sakamoto, "On the distributions of the product and the quotient of the independent and uniformly distributed random variables," Tohoku Math. J. 49 (1943)."

  4. Uniform Distribution The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive.

  5. Probability density function • The probability density function of the continuous uniform distribution is:

  6. mfg. of Uniform Distribution  • From the definition of the continuous uniform distribution X has probability density function: From the definition of a moment generating function:

  7. Characteristics • The density function integrates to unity • Each of the inputs that go in to form the function have equal weighting • Mean of the uniform function is given by: • The variance is given by the equation:

  8. Mean of the uniform function

  9. The variance of the uniform function

  10. uniform distribution Pdf of uniform distribution: Cdf of uniform distribution:

  11. The plot of the uniform function • The plot of the uniform function is as below: The location of the interval has little influence in deciding if the uniformly distributed variable falls within the fixed length. Two factors that influence this the most are the interval size and the fact that the interval falls within the distributions support.

  12. Moments • The mean (first moment) of the distribution is: • The second moment of the distribution is: • n general, the n-th moment of the uniform distribution is:

  13. Types of uniform distribution • There are two types of uniform distributions: • discrete • continuous. • In the former type of distribution, each outcome is discrete. • In a continuous distribution, outcomes are continuous and infinite.

  14. Probability function

  15. Example

  16. Quick Summary • In statistics, uniform distribution is a probability distribution where all outcomes are equally likely. • Discrete uniform distributions have a finite number of outcomes. A continuous uniform distribution is a statistical distribution with an infinite number of equally likely measurable values.

  17. real life examples of uniform distribution • the position of a particular air molecule in a room • the point on a car tyre where the next puncture will occur, • the number of seconds past the minute that the current time is • the length of time that one may have to wait for a train. •  imagine a man standing on a street corner handing a $50 bill to a lucky passerby. If it were completely random, then every person that walked by would have an equal chance of getting the $50 bill. • The day of the week of the hottest day of a year is about equally likely to be any of the seven days. 

  18. advantages • The probabilities for uniform distribution function are simple to calculate due to the simplicity of the function form. Therefore, there are various applications that this distribution can be used for as shown below: hypothesis testing situations, random sampling cases, finance, etc. Furthermore, generally, experiments of physical origin follow a uniform distribution (e.g.. emission of radioactive particles). However, it is important to note that in any application, there is the unchanging assumption that the probability of falling in an interval of fixed length is constant.

  19. applications • Standard uniform distribution: If a =0  and b=1 then the resulting function is called a standard uniform distribution. This has very important practical applications. • There are variables in physical, management and biological sciences that have the properties of a uniform distribution and hence it finds application is these fields.

  20. Thank you

More Related