Genetibase.MathX Namespace
Namespace hierarchy
Classes
| Class |
Description |
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NuGenBinomialProbability
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When to use a BinomialProbability: Use when you need to ask the question, "If the chance of something happening is P percent, what is the probability it will happen Y times out of N attempts." Example: Die rolling. If the chance to roll a one is 1/6 or 16.7%, what is the probability it will happen 3 times out of 5 rolls. Notes: The event must be a discrete event like rolling a die, flipping a coin, or pulling a card. Events that consider an average percentage that it will happen or if each trial in turn affects the percentage that the event will happen are not modeled by the binomial probability distribution but can give meaningful estimates. ex: A basketball player has a free throw percentage of 70%. What is the probability he makes his next two free throw shots. His first shot would then change his free throw percentage by a small amount but if this fact is omitted the answer is relatively the same. |
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NuGenBox2DTest
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NuGenComplexLib
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Complex Number Operations |
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NuGenDistributions
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Numerical computation of special distributions |
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NuGenErrorLib
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The error class |
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NuGenFractionException
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Exception class for NuGenFraction, derived from System.Exception |
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NuGenGeometricProbability
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When to use a Geometric probability : The geometric probability asks the question, "Given the chance that each trial being successful is the same, what is the probability that the first success happens on a the Yth trial." This can be referred to as a russian roulette type of question. If a revolver holds one bullet out of six chambers the chance for each trial is the same. The probability answers the percentage that bullet will go off in each successive round given all the previous rounds were unsuccesful. This can be seen as the simple multiplication rule of probability, for example, P(Y=3) = chance of failure * chance of failure * chance of success = 5/6 * 5/6 * 1/6 = 25/216 or about 2% |
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NuGenHyperGeometricProbability
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When to use the HyperGeometricProbability This probability is the one used to compute odds in many of the lotterys in the United States. It is used when you are picking from two sets in a mixed population. The basic example is a bag filled with red and black chips. 5 red chips and 4 black ones. You are asked to choose 3 chips without looking. What is the chance you will pick exactly two black chips. If you look below you will see the construction parameters. The population size, N, is 4 + 5 = 9. The sample size, n, is 3 since we are picking 3 chips. The sample set we are interested in is black chips which there are 3 of so r = 3. And finally the random variable, y, is 2, the number of black chips we want to choose out of 3 pulls. To compute lottery odds lets assume the lottery in question has 50 numbers and they choose 6 of them at random live on television. So we know N = 50 and the sample size n=6. You have 6 numbers you paid money for that you are interested in, these six numbers represent the selected set r, r = 6. Now for the grand payoff, getting all six numbers you need all picked numbers to be in your selected set. y = 6. Often there is a lesser payout for 5 numbers which you could compute by changing y = 5. Finally you usually win your money back if you match two numbers so here y = 2. To find the chance of winning anything you would compute P(y < =6) - P(y=1) since usually matching one number has no payout. Many lotterys use an extra number affectionately called a mega number or some sort which is separate from the regular 50 or so numbers. This last number is computed by a regular BinomialProbability and multiplied against the previous result for six numbers (since the events are independent) to get the odds of winning. |
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NuGenLinearRegression
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Linear Regression |
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NuGenLinearSystemSolver
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Solves the linear equation system [A]{x}={b} for {x} and calculates the determinant of matrix [A] |
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NuGenLogaritmicFunctions
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Logarithmic and Other Functions |
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NuGenMatrix
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NuGenMatrix provides basic operations with matrices |
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NuGenMatrixOperations
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Vector and matrix operations |
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NuGenNegativeBinomialProbability
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When to use the NuGenNegativeBinomialProbability The Negative Binomial NuGenProbability is similar to the Geometric NuGenProbability in concept but similar to the Binomial NuGenProbability in computation. The Negative Binomial probability answers the question, "What is the chance that the Kth successful trial happens on the Yth trial. For example, Die rolling, what is the chance of rolling a one EXACTLY three times with the last one happening on the sixth roll. Here K=3, Y=6 and the chance to roll a one is 1/6 |
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NuGenPoissonProbability
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When to use the Poisson probability Use when you have events that can happen instantaneously and at any time. The chance of two or more events happening at the same time is effectively zero for a time span small enough. For example: A certain street corner has an average of 7 traffic accidents per year. What is the probability that there will be 8 accidents the following year. Here our lambda is 7, the average from which we base the likelihood of traffic accidents happening in a year. Our random variable is 8. The probability will be less than if our random variable was 7 and more than if our random variable was 9. This probability distribution has a bell shaped curve to it. |
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NuGenPolynomial
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Polynomial Operations |
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NuGenProbability
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NuGenQuadratic
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Quadratic |
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NuGenSignedLogical
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Signed Logical Functions |
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NuGenStatistics
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computational statistics |
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NuGenSystemsOfCoordinates
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Systems of Coordinates |
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NuGenTrigFunctions
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Trigonometric functions |
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NuGenTrigonometry
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Trigonometry Functions |
Structures
Enumerations