Concept of Kurtosis, Business Mathematics & Statistics Notes Study Business Mathematics and Statistics B Com

Ans.1 When data are approximately normally distributed, which means they follow a bell shape but the population variance is unknown, the t-distribution is used. The variance of a t-distribution is estimated using the data set’s degrees of freedom . In the 2- and 3-year study periods, stocks with positive skewness and low kurtosis outperformed the BSE500 index by a substantial margin.

Important measures of central tendency – arithmetic mean median and mode.Relative merits and demerits of these measures. Important measures of dispersion, Range, MeanDeviation, Variance and Standard Deviation. Relative merits and demerits of these measures.Coefficient of variation; Normal Curve, Concepts of Skewness and kurtosis. Basic concept of samplingdistribution; standard error and central limit theorem. Introduction to statistical inference, generalprinciples of testing of hypothesis, types of errors.

Just upload your form 16, claim your deductions and get your acknowledgment number online. You can efile income tax return on your income from salary, house property, capital gains, business & profession and income from other sources. Further you can also file TDS returns, generate Form-16, use our Tax Calculator software, claim HRA, check refund status and generate rent receipts for Income Tax Filing. Let us look at the number observed when rolling two regular six-sided dice, as a basic example of a probability distribution. Every die has a 1/6 chance of rolling any single number, one through six.

TaxCloud (Direct Tax Software)

The coefficient of skewness is used to compare a sample distribution to a normal one. If the value is very large it implies that there is a greater difference between the sample distribution as compared to a normal distribution. The probability distribution most widely used is the standard distribution, which is often used in banking, business, research, and engineering.

A that there is one number that best summarizes the entire set of measurements, a number that is in some way “central” to the set. Statistics is a science that finds its place virtually in all science and research fields in order to manage and improve data. Statisticians have been using different mathematical and computational tools to study this science.

One measure of skewness would be to subtract the mean from the mode, then divide the difference by the Standard Deviation of the data. We have a dimensionless quantity as the explanation for dividing the difference. This explains why there is positive skewness in data skewed to the right. The mean is greater than the mode if the data set is skewed to the right, so subtracting the mode from the mean gives a positive number. A similar argument shows why there is negative skewness in data skewed to the left. The closeness of such distributions to normal is determined by sample size and degree of non-normality of the info-producing course of that produces the person data values.

But the basis of this theory lies in the techniques that a data scientist uses to analyze that data to make predictions further. So, a data scientist first tries to understand the data by applying descriptive statistics in data science involves summarizing and organizing the data so they can be easily understood. Descriptive statistics in data science, unlike inferential statistics, seeks to describe the data but does not attempt to make inferences from the sample to the whole population. It is the flatness or peakedness of a histogram of a frequency distribution. It shows how peaked the central values are in a distribution of data sets.

More Measurement and Analysis of Data Questions

Moreover Kurtosis shows the pickedness of Normal Probability curve, it doesn’t decide the usually of distribution. A distribution with kurtosis greater than three is leptokurtic and a distribution with kurtosis less than three is platykurtic. The measure of skewness is applied very commonly since skewed data is seen quite often in different situations. In commerce, the skewness has to be measured very frequently when incomes are skewed to the right or to the left.

Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution. That is, data sets with high kurtosis tend to have heavy tails, or outliers. Data sets with low kurtosis tend to have light tails, or lack of outliers. Kurtosis is a measure of the “tailedness” of the probability distribution. A standard normal distribution has kurtosis of 3 and is recognized as mesokurtic. The measure of the asymmetry of a distribution of probability that is ideally symmetric and is given by the third standardized moment is skewness.

Thus this histogram plot confirms the normality test results from the two tests in this article. In order to generate the histogram plot, follow the below procedure. Ignoring such extreme observations can create risks that are not captured by financial models based on normal distribution. When data follows normal distribution, the kurtosis has a value of three. Value greater than three means higher instances of abnormal returns, whereas low value of kurtosis implies fewer instances of abnormal returns. In a negatively skewed distribution the value of mode is maximum and that of mean least-the median lies in between the two.

Chapter 4 – Discussed about Moments ,skewness ,kurtosis

And there is a very less number of students who scored very high marks. We can conclude that the test was very difficult and there are very few good students who scored high marks and these students can be considered outliers as they are not following the general trend. The difference between two means hypothesis is tested with dependent samples. The number of independent observations is equal to the sample size minus one when estimating a mean score or a proportion from a single sample. The time series result will identify the residuals from the regression analysis. A distribution which is more peaked than Normal distribution is called Leptokurtic distribution.

• Lower values result in heavier tails, while higher values cause the T distribution to resemble a standard normal distribution with one standard deviation and zero mean.
• Data Science is the one that analyzes the data and makes predictions.
• This range is bounded between the minimum and maximum possible values.

To standardise the value, the t distribution formula subtracts the sample mean from the population mean, divides by standard deviation, and multiplies by the square root of the sample size. Condensation of data is necessary in statistical analysis because a large number of big figures are not only confusing for the mind but are also lifficult to analyse also. The preceding articles showed how to conduct time series analysis in STATA on a range of univariate and multivariate models including ARIMA, VAR and VECM . Time series data requires some diagnostic tests in order to check the properties of the independent variables.

What is the measure of Spread / Dispersion?

Although the concepts are difficult to comprehend for the lay investor, you can easily calculate skewness and kurtosis using the MS excel functions Skew and Kurt. Standard deviation is a common statistical tool used to estimate the total risk of a stock or an index. It is used by financial analysts to estimate the range within which a stock or an index returns are likely to fall. For example, after analyzing the data, a sneaker store decided that one of the most favoured sneaker types is Type-A. In the next chapter, we will continue our discussion of statistical measures of risk by talking about covariance and correlation.

The end result advised the deviation of information from normality was not severe as the value of skewness and kurtosis index were below 3 and 10 respectively . If your primary concern is kurtosis, KS test is fine (I’m utilizing it very successfully). The worth is often compared to the kurtosis of the traditional distribution, which is equal to three. If the kurtosis is bigger than three, then the dataset has heavier tails than a normal distribution . Kurtosis is usually used along side the skewness statistics to determine whether an output is roughly Normally distributed.

What Does a Zero Coefficient of Skewness Indicate?

Sample kurtosis that significantly deviates from 0 might indicate that the information usually are not usually distributed. Our examination discuss the concept of kurtosis of these categories will not be as precise as we could be if we used the technical mathematical definition of kurtosis.

Skewness is used as an alternative risk measurement tool when the data is exhibits asymmetrical distribution. A stock with negative skewness is one that generates frequent small gains and few extreme or significant losses in the time period considered. On the other hand, a stock with positive skewness is one that generates frequent small losses and few extreme gains. If a stock’s return follows a normal distribution pattern, then their will be no skewness. Investors use probability distribution to predict returns overtime on assets, such as securities and to hedge their risk.

There are several normality tests such as the Skewness Kurtosis test, the Jarque Bera test, the Shapiro Wilk test, the Kolmogorov-Smirnov test, and the Chen-Shapiro test. This article shows two tests; Skewness Kurtosis and Jarque Bera tests because they are simple and popular. The coefficient of skewness using the median is a more robust measure of skewness than the coefficient that is calculated using the mode. The coefficient of skewness can be defined as a measure of skewness that indicates the strength and the direction of asymmetry in a probability distribution. If the value of the mean, median, and mode are equal then the distribution is a normal distribution and the coefficient of skewness will be 0.