Sampling Distribution
A sampling distribution is a probability distribution of a statistic obtained through a large number of samples drawn from a specific population. The sampling distribution of a given population is the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population. It’s a type of distribution that involves the probability distribution of sample statistics based on a randomly selected sample. Sampling distribution arises from a group of selected data that is calculated using various statistics such as Mean, Median, Mode, Standard deviation and Range. This distribution is useful in testing a hypothesis.
Frequency Distribution
In statistics, a frequency distribution is a table that displays the frequency of various outcomes in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval, and in this way, the table summarizes the distribution of values in the sample.
An example of univariate frequency distribution table
|
Degree of agreement
|
Number
|
|
|
1
|
Strongly agree
|
20
|
|
2
|
Agree somewhat
|
30
|
|
3
|
Not sure
|
20
|
|
4
|
Disagree somewhat
|
15
|
|
5
|
Strongly disagree
|
15
|
A frequency distribution shows us a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in a class. It is a way of showing unorganized data. For example, to show results of an election, the income of people for a certain region, sales of a product within a certain period, student loan amounts of graduates, etc. Some of the graphs that can be used with frequency distributions are histograms, line charts, bar charts and pie charts. Frequency distributions are used for both qualitative and quantitative data.
Population Distribution
The Population Distribution is a form of probability distribution that measures the frequency with which the items or variables that make up the population are drawn or expected to be drawn for a given research study.
The characteristics or attributes of the population, i.e. the value of each variable in the population can be determined only when the investigator completely enumerates all the items of the population using the census method. By doing so, the frequency of these characteristics, i.e. probability of selecting some particular characteristic from the population, can be determined.
In case the population size is large and its complete enumeration is not possible, then the representative samples can be selected from the population. By doing so, several cases falling in several classes or categories can be observed to determine the frequency with which the cases of particular classes are likely to be drawn from the sample.
Once the complete information about the population is gathered, it is believed that the investigator has the knowledge of the population mean and standard deviation. For example, if a company has manufactured 5,000 cars in 2013 and want to gather information about those who had bought it and their experience so far. On the basis of such information, we can compute the population means and standard deviation (σ).
Probability Distribution
In probability and statistics, a probability distribution is a mathematical description of a random phenomenon in terms of the probabilities of events. Examples of random phenomena include the results of an experiment or survey. A probability distribution is defined in terms of an underlying sample space, which is the set of all possible outcomes of the random phenomenon being observed. The sample space may be the set of real numbers or a higher-dimensional vector space, or it may be a list of non-numerical values. Probability distributions are generally divided into two classes. A discrete probability distribution can be encoded by a list of the probabilities of the outcomes, known as a probability mass function. On the other hand, in a continuous probability distribution, the probability of any individual outcome is 0. Continuous probability distributions can often be described by probability density functions; however, more complex experiments, such as those involving stochastic processes defined in continuous time, may demand the use of more general probability measures.
In applied probability, a probability distribution can be specified in a number of different ways, often chosen for mathematical convenience:
- by supplying a valid probability mass function or probability density function
- by supplying a valid cumulative distribution function or survival function
- by supplying a valid hazard function
- by supplying a valid characteristic function
- by supplying a rule for constructing a new random variable from other random variables whose joint probability distribution is known.
A probability distribution whose sample space is the set of real numbers is called univariate, while a distribution whose sample space is a vector space is called multivariate. A univariate distribution gives the probabilities of a single random variable taking on various alternative values; a multivariate distribution (a joint probability distribution) gives the probabilities of a random vector—a list of two or more random variables—taking on various combinations of values. Important and commonly encountered univariate probability distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution. The multivariate normal distribution is a commonly encountered multivariate distribution.
No comments:
Post a Comment