Statistics Probability Bayes Theorem – lesscss

Statistics – Probability Bayes Theorem One of the most significant developments in the probability field has been the development of Bayesian decision theory which has proved to be of immense help in making decisions under uncertain conditions. The Bayes Theorem was developed by a British Mathematician Rev. Thomas Bayes. The probability given under Bayes theorem… 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 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 Process Capability (Cp) & Process Performance (Pp) – lesscss

Statistics – Process Capability (Cp) & Process Performance (Pp) Process Capability Formula Example Process Performance Formula Process Capability Process capability can be defined as a measurable property of a process relative to its specification. It is expressed as a process capability index ${C_p}$. The process capability index is used to check the variability of the… Read More »

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Statistics Poisson Distribution – lesscss

Statistics – Poisson Distribution Poisson conveyance is discrete likelihood dispersion and it is broadly use in measurable work. This conveyance was produced by a French Mathematician Dr. Simon Denis Poisson in 1837 and the dissemination is named after him. The Poisson circulation is utilized as a part of those circumstances where the happening’s likelihood of… Read More »

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Statistics Grand Mean – lesscss

Statistics – Grand Mean When sample sizes are equal, in other words, there could be five values in each sample, or n values in each sample. The grand mean is the same as the mean of sample means. Formula Example Formula ${X_{GM} = frac{sum x}{N}}$ Where − ${N}$ = Total number of sets. ${sum x}$… Read More »

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Statistics Harmonic Number – lesscss

Statistics – Harmonic Number Harmonic Number is the sum of the reciprocals of the first n natural numbers. It represents the phenomenon when the inductive reactance and the capacitive reactance of the power system becomes equal. Formula Example Formula ${ H = frac{W_r}{W} \[7pt] , where W_r = sqrt{ frac{1}{LC}} } \[7pt] , and W… 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 Negative Binomial Distribution – lesscss

Statistics – Negative Binomial Distribution Negative binomial distribution is a probability distribution of number of occurences of successes and failures in a sequence of independent trails before a specific number of success occurs. Following are the key points to be noted about a negative binomial experiment. The experiment should be of x repeated trials. Each… 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 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 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 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 Process Sigma – lesscss

Statistics – Process Sigma Process sigma can be defined using following four steps: Measure opportunities, Measure defects, Calculate yield, Look-up process sigma. Formulae Used Example Formulae Used ${DPMO = frac{Total defect}{Total Opportunities} times 1000000}$ ${Defect (%) = frac{Total defect}{Total Opportunities} times 100}$ ${Yield (%) = 100 – Defect (%) }$ ${Process Sigma = 0.8406+sqrt{29.37}-2.221 times… Read More »

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Statistics Kolmogorov Smirnov Test – lesscss

Statistics – Kolmogorov Smirnov Test This test is used in situations where a comparison has to be made between an observed sample distribution and theoretical distribution. K-S One Sample Test Formula Example K-S Two Sample Test Formula K-S One Sample Test This test is used as a test of goodness of fit and is ideal… Read More »

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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 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 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 Mcnemar Test – lesscss

Statistics – Mcnemar Test Mc Nemer test is utilized for two related examples as a part of circumstances where the states of mind of individuals are noted previously, then after the fact treatment to test the essentialness of progress in sentiment if any. The Mc Nemer test is especially helpful when the information speaks the… Read More »

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Statistics Outlier Function – lesscss

Statistics – Outlier Function An outlier in a probability distribution function is a number that is more than 1.5 times the length of the data set away from either the lower or upper quartiles. Specifically, if a number is less than ${Q_1 – 1.5 times IQR}$ or greater than ${Q_3 + 1.5 times IQR}$, then… Read More »

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