Normal Distribution. in probability theory, the normal (or Gaussian) distribution is a continuous probability distribution that has a bell-shaped probability.

Презентация:



Advertisements
Похожие презентации
Chap 8-1 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chapter 8 Estimation: Single Population Statistics for Business and Economics.
Advertisements

Correlation. In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to.
Statistics Probability. Statistics is the study of the collection, organization, analysis, and interpretation of data.[1][2] It deals with all aspects.
Benford Benford's law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading.
Chap 7-1 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chapter 7 Sampling and Sampling Distributions Statistics for Business.
Chap 15-1 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chapter 15 Nonparametric Statistics Statistics for Business and Economics.
Chap 9-1 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chapter 9 Estimation: Additional Topics Statistics for Business and Economics.
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap 1-1 Chapter 1 Why Study Statistics? Statistics for Business and Economics.
Chap 11-1 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chapter 11 Hypothesis Testing II Statistics for Business and Economics.
SIR model The SIR model Standard convention labels these three compartments S (for susceptible), I (for infectious) and R (for recovered). Therefore, this.
Knot theory. In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a.
Business Statistics 1-1 Chapter Two Describing Data: Frequency Distributions and Graphic Presentation GOALS When you have completed this chapter, you will.
Exponential function. In mathematics, the exponential function is the function ex, where e is the number (approximately ) such that the function.
Econometrics. Econometrics is "the application of mathematics and statistical methods to economic data" and described as the branch of economics "that.
Polynomial In mathematics, a polynomial is an expression of finite length constructed from variables (also called indeterminates) and constants, using.
Chap 3-1 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chapter 3 Describing Data: Numerical Statistics for Business and Economics.
Logarithm The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm.
Time-Series Analysis and Forecasting – Part IV To read at home.
Why do we learn English at schools. (by Kurdina Ekaterina) Learning a new language often begins at a young age and, at some schools, is continued throughout.
In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting (rearranging) objects.
Транксрипт:

Normal Distribution

in probability theory, the normal (or Gaussian) distribution is a continuous probability distribution that has a bell-shaped probability density function, known as the Gaussian function or informally the bell curve

The normal distribution is considered the most prominent probability distribution in statistics. There are several reasons for this:[1] First, the normal distribution arises from the central limit theorem, which states that under mild conditions the mean of a large number of random variables drawn from the same distribution is distributed approximately normally, irrespective of the form of the original distribution. This gives it exceptionally wide application in, for example, sampling. Secondly, the normal distribution is very tractable analytically, that is, a large number of results involving this distribution can be derived in explicit form.

For these reasons, the normal distribution is commonly encountered in practice, and is used throughout statistics, natural sciences, and social sciences[2] as a simple model for complex phenomena. For example, the observational error in an experiment is usually assumed to follow a normal distribution, and the propagation of uncertainty is computed using this assumption. Note that a normally-distributed variable has a symmetric distribution about its mean.

Quantities that grow exponentially, such as prices, incomes or populations, are often skewed to the right, and hence may be better described by other distributions, such as the log-normal distribution or Pareto distribution. In addition, the probability of seeing a normally-distributed value that is far (i.e. more than a few standard deviations) from the mean drops off extremely rapidly.

As a result, statistical inference using a normal distribution is not robust to the presence of outliers (data that is unexpectedly far from the mean, due to exceptional circumstances, observational error, etc.). When outliers are expected, data may be better described using a heavy-tailed distribution such as the Student's t-distribution.