Tag Archives: Python

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 »

Statistics Gamma Distribution – lesscss

Statistics – Gamma Distribution The gamma distribution represents continuous probability distributions of two-parameter family. Gamma distributions are devised with generally three kind of parameter combinations. A shape parameter $ k $ and a scale parameter $ theta $. A shape parameter $ alpha = k $ and an inverse scale parameter $ beta = frac{1}{… Read More »

Statistics Dot Plot – lesscss

Statistics – Dot Plot A dot chart or dot plot is a statistical chart consisting of data points plotted on a fairly simple scale, typically using filled in circles. Example Problem Statement: A study of “To what extent does it take you to have breakfast?” has these outcomes: Minutes 0 1 2 3 4 5… Read More »

Statistics Frequency Distribution – lesscss

Statistics – Frequency Distribution Frequency distribution is a table that displays the frequency of various outcomes in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval, and in this way, the table summarizes the distribution of values in the sample. Example… Read More »

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 »

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 Probability density function of F distribution is given as: Formula ${ f(x; d_1, d_2) = frac{sqrt{frac{(d_1… Read More »

Statistics Factorial – lesscss

Statistics – Factorial Factorial is a function applied to natural numbers greater than zero. The symbol for the factorial function is an exclamation mark after a number, like this: 2! Formula ${n! = 1 times 2 times 3 … times n}$ Where − ${n!}$ = represents factorial ${n}$ = Number of sets Example Problem Statement:… Read More »

Statistics Power Calculator – lesscss

Statistics – Power Calculator Whenever a hypothesis test is conducted, we need to ascertain that test is of high qualitity. One way to check the power or sensitivity of a test is to compute the probability of test that it can reject the null hypothesis correctly when an alternate hypothesis is correct. In other words,… Read More »

Statistics Pooled Variance (r) – lesscss

Statistics – Pooled Variance (r) Pooled Variance/Change is the weighted normal for assessing the fluctuations of two autonomous variables where the mean can differ between tests however the genuine difference continues as before. Example Problem Statement: Compute the Pooled Variance of the numbers 1, 2, 3, 4 and 5. Solution: Step 1 Decide the normal… Read More »

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 »

Statistics One Proportion Z Test – lesscss

Statistics – One Proportion Z Test The test statistic is a z-score (z) defined by the following equation. ${z = frac{(p – P)}{sigma}}$ where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and ${sigma}$ is the standard deviation of the sampling distribution. Test Statistics is defined… Read More »

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 »

Statistics Mean Deviation – lesscss

Statistics – Mean Deviation Referred to as average deviation, it is defined as the sum of the deviations(ignoring signs) from an average divided by the number of items in a distribution The average can be mean, median or mode. Theoretically median is d best average of choice because sum of deviations from median is minimum,… Read More »

Statistics Probability Multiplicative Theorem – lesscss

Statistics – Probability Multiplicative Theorem For Independent Events The theorem states that the probability of the simultaneous occurrence of two events that are independent is given by the product of their individual probabilities. ${P(A and B) = P(A) times P(B) \[7pt] P (AB) = P(A) times P(B)}$ The theorem can he extended to three or… Read More »

Statistics Kurtosis – lesscss

Statistics – Kurtosis The degree of tailedness of a distribution is measured by kurtosis. It tells us the extent to which the distribution is more or less outlier-prone (heavier or light-tailed) than the normal distribution. Three different types of curves, courtesy of Investopedia, are shown as follows − It is difficult to discern different types… Read More »

Statistics Harmonic Mean – lesscss

Statistics – Harmonic Mean What is Harmonic Mean? Harmonic Mean is also a mathematical average but is limited in its application. It is generally used to find average of variables that are expressed as a ratio of two different measuring units e. g. speed is measured in km/hr or miles/sec etc. Weighted Harmonic Mean Formula… Read More »

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 ${ f = frac{1}{2 pi sqrt{LC}} } $ Where − ${f}$ = Harmonic resonance frequency. ${L}$ = inductance of the load. ${C}$ = capacitanc of the… Read More »

Statistics Probability Additive Theorem – lesscss

Statistics – Probability Additive Theorem 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 cup B) = P(A) + P(B)}$ The theorem can he… Read More »

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 Odd permutation is a set of permutations obtained from odd number of two element swaps in a set.… Read More »

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 ${P(X=x) = p times q^{x-1} }$… Read More »