The probability distribution as a concept can occur in two ways, depending of the characteristics of your observation. It can be a probability density function (pdf) in case of a continous random variable that models the observation, or, if only discrete values of the random variable are possible, with the help of the so called probability mass function. For pdf you need to evaluate an integral to get your information. The pmf can deliver the information as a weighted sum. In both cases the area under the "curves" has to be unity. For the pmf this is accomplished modelling the "spikes" with the delta-function.
Probability density function: for a continuous random variable X, we can define the probability that X is in [a,b] as
P(a
Probability density function: for a continuous random variable X, we can define the probability that X is in [a,b] as
P(a
thanks.. a lot.. i agree with your answer. but some book write that The density is the derivative of the distribution function. is this true??? i am interested to know about how and where this concept came from?
The problem is that sometimes "probability distribution function" is used synonymously with "probability density function" and sometimes synonymously with "cumulative distribution function".
Have a look at the second paragraph here:
https://en.wikipedia.org/wiki/Probability_density_function
The probability density function (pdf) IS the derivative of the cumulative distribution function (cdf), and it appears that the book (s?) you're looking at are using the term that way.
The cdf is a probability (as Hiqmet correctly points out): cdf(v) is the probability that the random variable is less than or equal to v.
The pdf is the derivative of the cdf. You can get the probability that the random variable is between two values by doing a definite integral on the pdf between those two values. The pdf is generally what one thinks of when thinking of a "probabililty distribution". For a gaussian random variable, the pdf will be the one with the "bell curve" shape. The discrete equivalent of the pdf is a pmf (probability mass function). A histogram of realizations of a random variable will (presuming enough realizations and small enough bins) have a shape similar to the shape of the pdf.
Both are same first one is used in general and 2nd is used for continuous random variable case.
hello sir , Is there any code/expression by which we can find the probability distribution (PDD) in matlab/minitab, as i have a set of values (around 2lakhs , obtained from DSO) inorder to find the electrical characteristics of a welding unit. ?
Probability distribution function (PDF) is well-defined as a function over general sets of data where it may be a probability mass function (PMF) rather than the density. However, density function has also been used for PMF where it’s applicable in the context of discrete random variables. Whereas probability distribution function is applying in the context of continuous random variables.
There are different definitions in the literature somewhat confusing. But, in general:
- the probability density function (PDF) is used for continuous random variables;
- the a probability mass function (PMF) is used for discrete random variables;
and the probability distribution function is a general term that may refer to both PDF and PMF
- Probability Distribution Function represents the probability of a continuous random variable taking a specific value which is used for continuous random variables. For discrete random variables, the Probability Mass Function (PMF) is not applicable. But Probability Density Function is specifically for continuous probability distributions which describes the likelihood of a continuous random variable falling within a given range. The density (when it exists) is the derivative of the distribution function.
For ans, follow the link below:
https://www.quora.com/What-is-the-difference-between-probability-density-function-probability-mass-function-and-probability-distribution-function
The right term is probability density function (PDF) and not probability distribution function. ..when we integrate the PDF we will get the Cumulative Distribution Function hence the CDF.
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