Business statistics is the science of good decision making in the face of uncertainty and is used in many disciplines such as financial analysis, econometrics, auditing, production and operations including services improvement, and marketing research. ... en.wikipedia.org/wiki/Business_Statistics Why Study Statistics? Answer Statistics is a mathematical techniques used to analyze and manipulate data for getting answer to the issues / questions. Without knowing the statistics many data available in the current information age is not possible and the world can not live peacefully. Whether forecast makes us to be prepared for any natural calamities. One can not imagine how we can live in this world without whether forecast. Why Study Statistics? People study statistics because they need to quantify external events, summarize experiment or research results, make data comparisons, and establish correlations . answers.ask/Science/Psychology/ Statistical model From Wikipedia, the free encyclopedia A statistical model is a formalization of relationships between variables in the form of mathematical equations. A statistical model describes how one or more random variables are related to one or more other variables. The model is statistical as the variables are not deterministically but stochastically related. In mathematical terms, a statistical model is frequently thought of as a pair (Y, P) where Y is the set of possible observations and P the set of possible probability distributions on Y . It is assumed that there is a distinct element of P which generates the observed data. Statistical inference enables us to make statements about which element(s) of this set are likely to be the true one. Most statistical tests can be described in the form of a statistical model. For example, the Students t-test for comparing the means of two groups can be formulated as seeing if an estimated parameter in the model is different from 0. Another similarity between tests and models is that there are assumptions involved. Error is assumed to be normally distributed in most models.[1]. Model comparison[edit] Models can be compared to each other. This can either be done when you have done an exploratory data analysis or a confirmatory data analysis. In an exploratory analysis, you formulate all models you can think of, and see which describes your data best. In a confirmatory analysis you test which of your models you have described before the data was collected fits the data best, or test if your only model fits the data. In linear regression analysis you can compare the amount of variance explained by the independent variables, R2, across the different models. In general, you can compare models that are nested by using a Likelihood-ratio test. Nested models are models that can be obtained by restricting a parameter in a more complex model to be zero. Classification According to the number of the endogenous variables and the number of equations, models can be classified as complete models (the number of equations equal to the number of endogenous variables) and incomplete models. Some other statistical models are the general linear model (restricted to continuous dependent variables), the generalized linear model (for example, logistic regression), the multilevel model, and the structural equation model.[2] Quantitative Methods - Skew And Kurtosis Skew Skew, or skewness, can be mathematically defined as the averaged cubed deviation from the mean divided by the standard deviation cubed. If the result of the computation is greater than zero, the distribution is positively skewed. If its less than zero, its negatively skewed and equal to zero means its symmetric. For interpretation and analysis, focus on downside risk. Negatively skewed distributions have what statisticians call a long left tail (refer to graphs on previous page), which for investors can mean a greater chance of extremely negative outcomes. Positive skew would mean frequent small negative outcomes, and extremely bad scenarios are not as likely. A nonsymmetrical or skewed distribution occurs when one side of the distribution does not mirror the other. Applied to investment returns, nonsymmetrical distributions are generally described as being either positively skewed (meaning frequent small losses and a few extreme gains) or negatively skewed (meaning frequent small gains and a few extreme losses). Positive Skew Negative Skew Figure 2.4 For positively skewed distributions, the mode (point at the top of the curve) is less than the median (the point where 50% are above/50% below), which is less than the arithmetic mean (sum of observations/number of observations). The opposite rules apply to negatively skewed distribution: mode is greater than median, which is greater than arithmetic mean. Positive: Mean > Median > Mode Negative: Mean < Median < Mode Notice that by alphabetical listing, its mean à median à mode. For positive skew, they are separated with a greater than sign, for negative, less than Skewness The first thing you usually notice about a distribution’s shape is whether it has one mode (peak) or more than one. If it’s unimodal (has just one peak), like most data sets, the next thing you notice is whether it’s symmetric or skewed to one side. If the bulk of the data is at the left and the right tail is longer, we say that the distribution is skewed right or positively skewed; if the peak is toward the right and the left tail is longer, we say that the distribution is skewed left or negatively skewed. Look at the two graphs below. They both have μ = 0.6923 and σ = 0.1685, but their shapes are different. beta(4.5,2) distribution, with skewness minus 0.5370 Beta(α=4.5, β=2) skewness = −0.5370 1.3846 minus beta(4.5,2) distribution, with skewness plus 0.5370 1.3846 − Beta(α=4.5, β=2) skewness = +0.5370
Posted on: Sun, 16 Mar 2014 09:18:50 +0000
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