Statistics Histograms – lesscss

Statistics – Histograms A histogram is a graphical representation of the distribution of numerical data. It is an estimate of the probability distribution of a continuous variable (quantitative variable). Problem Statement: Every month one measure the amount of weight one’s dog has picked up and get these outcomes: 0.5 0.5 0.3 -0.2 1.6 0 0.1… Read More »

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Statistics Gumbel Distribution – lesscss

Statistics – Gumbel Distribution Gumbel Distribution represents the distribution of extreme values either maximum or minimum of samples used in various distributions. It is used to model distribution of peak levels. For example, to show the distribution of peak temperatures of the year if there is a list of maximum temperatures of 10 years. Probability… Read More »

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Statistics Logistic Regression – lesscss

Statistics – Logistic Regression Logistic regression is a statistical method for analyzing a dataset in which there are one or more independent variables that determine an outcome. The outcome is measured with a dichotomous variable (in which there are only two possible outcomes). Formula Example Formula ${pi(x) = frac{e^{alpha + beta x}}{1 + e^{alpha +… Read More »

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Statistics Probability Additive Theorem – lesscss

Statistics – Probability Additive Theorem For Mutually Exclusive Events Example For Non-Mutually Exclusive Events Example For Mutually Exclusive Events The additive theorem of probability states if A and B are two mutually exclusive events then the probability of either A or B is given by ${P(A or B) = P(A) + P(B) \[7pt] P (A… Read More »

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Statistics F distribution – lesscss

Statistics – F distribution The F distribution (Snedecor’s F distribution or the FisherSnedecor distribution) represents continuous probability distribution which occurs frequently as null distribution of test statistics. It happens mostly during analysis of variance or F-test. Probability density function Formula Cumulative distribution function Formula Probability density function Probability density function of F distribution is given… Read More »

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Statistics Hypergeometric Distribution – lesscss

Statistics – Hypergeometric Distribution A hypergeometric random variable is the number of successes that result from a hypergeometric experiment. The probability distribution of a hypergeometric random variable is called a hypergeometric distribution. Hypergeometric distribution is defined and given by the following probability function: Formula Example Formula ${h(x;N,n,K) = frac{[C(k,x)][C(N-k,n-x)]}{C(N,n)}}$ Where − ${N}$ = items in… Read More »

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Statistics Hypothesis testing – lesscss

Statistics – Hypothesis testing A statistical hypothesis is an assumption about a population which may or may not be true. Hypothesis testing is a set of formal procedures used by statisticians to either accept or reject statistical hypotheses. Statistical hypotheses are of two types: Null hypothesis, ${H_0}$ – represents a hypothesis of chance basis. Alternative… Read More »

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Statistics Geometric Probability Distribution – lesscss

Statistics – Geometric Probability Distribution The geometric distribution is a special case of the negative binomial distribution. It deals with the number of trials required for a single success. Thus, the geometric distribution is a negative binomial distribution where the number of successes (r) is equal to 1. Formula Example Formula ${P(X=x) = p times… Read More »

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Statistics Deciles Statistics – lesscss

Statistics – Deciles Statistics A system of dividing the given random distribution of the data or values in a series into ten groups of similar frequency is known as deciles. Formula Example Formula ${D_i = l + frac{h}{f}(frac{iN}{10} – c); i = 1,2,3…,9}$ Where − ${l}$ = lower boundry of deciles group. ${h}$ = width… Read More »

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Statistics Harmonic Resonance Frequency – lesscss

Statistics – Harmonic Resonance Frequency Harmonic Resonance Frequency represents a signal or wave whose frequency is an integral multiple of the frequency of a reference signal or wave. Formula Example Formula ${ f = frac{1}{2 pi sqrt{LC}} } $ Where − ${f}$ = Harmonic resonance frequency. ${L}$ = inductance of the load. ${C}$ = capacitanc… Read More »

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Statistics Goodness of Fit – lesscss

Statistics – Goodness of Fit The Goodness of Fit test is used to check the sample data whether it fits from a distribution of a population. Population may have normal distribution or Weibull distribution. In simple words, it signifies that sample data represents the data correctly that we are expecting to find from actual population.… Read More »

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Statistics Normal Distribution – lesscss

Statistics – Normal Distribution A normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme. Height is one simple example of something that follows a normal distribution pattern: Most people are of average height the numbers… Read More »

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Statistics Odd and Even Permutation – lesscss

Statistics – Odd and Even Permutation Consider X as a finite set of at least two elements then permutations of X can be divided into two category of equal size: even permutation and odd permutation. Odd Permutation Example Step 1: Step 2: Even Permutation Example Step 1: Step 2: Odd Permutation Odd permutation is a… Read More »

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Statistics Multinomial Distribution – lesscss

Statistics – Multinomial Distribution A multinomial experiment is a statistical experiment and it consists of n repeated trials. Each trial has a discrete number of possible outcomes. On any given trial, the probability that a particular outcome will occur is constant. Formula Example Formula ${P_r = frac{n!}{(n_1!)(n_2!)…(n_x!)} {P_1}^{n_1}{P_2}^{n_2}…{P_x}^{n_x}}$ Where − ${n}$ = number of events… Read More »

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Statistics Data Patterns – lesscss

Statistics – Data Patterns Data patterns are very useful when they are drawn graphically. Data patterns commonly described in terms of features like center, spread, shape, and other unusual properties. Other special descriptive labels are symmetric, bell-shaped, skewed, etc. Center Spread Shape Unusual Features Center The center of a distribution, graphically, is located at the… Read More »

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Statistics Inverse Gamma Distribution – lesscss

Statistics – Inverse Gamma Distribution Inverse Gamma Distribution is a reciprocal of gamma probability density function with positive shape parameters $ {alpha, beta } $ and location parameter $ { mu } $. $ {alpha } $ controls the height. Higher the $ {alpha } $, taller is the probability density function (PDF). $ {beta… Read More »

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Statistics Permutation with Replacement – lesscss

Statistics – Permutation with Replacement Each of several possible ways in which a set or number of things can be ordered or arranged is called permutation Combination with replacement in probability is selecting an object from an unordered list multiple times. Permutation with replacement is defined and given by the following probability function: Formula Example… Read More »

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Statistics Linear regression – lesscss

Statistics – Linear regression Once the degree of relationship between variables has been established using co-relation analysis, it is natural to delve into the nature of relationship. Regression analysis helps in determining the cause and effect relationship between variables. It is possible to predict the value of other variables (called dependent variable) if the values… Read More »

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Statistics Permutation – lesscss

Statistics – Permutation A permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement. For example, suppose we have a set of three letters: A, B, and C. we might ask how many ways we can arrange 2 letters from that set. Permutation is… Read More »

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Statistics F Test Table – lesscss

Statistics – F Test Table F-test is named after the more prominent analyst R.A. Fisher. F-test is utilized to test whether the two autonomous appraisals of populace change contrast altogether or whether the two examples may be viewed as drawn from the typical populace having the same difference. For doing the test, we calculate F-statistic… Read More »

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