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Quantitative methods for intuitive understandings
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Numerical Solutions to Linear and Nonlinear Equations | Logical Intuitions
https://blacklen.wordpress.com/2011/05/01/numerical-solutions-to-linear-and-nonlinear-equations
Numerical Solutions to Linear and Nonlinear Equations. Numerical solutions give easy and fast way to the answers to linear and nonlinear equations problems. There are several algorithms for this purpose, but this post will only introduce 2 ways; bisection method and Newton’s method. These are very common and popular for their own properties; bisection method is slow but always converges to the true answer, and Newton’s method is extremely quick to converge but sometimes fails. Leave a Reply Cancel reply.
Johnson-SU Distribution | Logical Intuitions
https://blacklen.wordpress.com/2011/04/23/johnson-su-distribution
Notation: J-SU(γ, σ, λ, ξ). Type: Unbound / infinite / asymmetric / continuous. Number of Parameters: 4. Use: Alternative to normal distribution. Support: x (- , ). Parameters: γ R, 0 σ, 0 λ, ξ R. 160; where. Where Φ is cdf of standard normal distribution. Pdf and cdf of Johnson-SU distribution. Johnson-SU distribution is closely related to normal distribution. Consider a Gaussian distribution. Its pdf can be, for properties of hyperbolic functions, written as below;. Note here Z and z are NOT.
Numerical Integration | Logical Intuitions
https://blacklen.wordpress.com/2011/04/30/numerical-integration
Numerical integration is implemented to compute integral of functions which are too hard or impossible. There is a lot of algorithms and it may be impossible to examine all of them on this blog. Here is the simplest algorithm for this purpose, Trapezoidal rule. The concept is basically modification of Riemann’s integral. For example, see a chart below;. It shows how to compute integral on the interval [a, b] by Trapezoidal rule. Formally, it is defined as. 2 thoughts on “Numerical Integration”. I learned...
ARCH and GARCH model for volatility estimation | Logical Intuitions
https://blacklen.wordpress.com/2010/09/22/arch-and-garch-model-for-volatility-estimation
ARCH and GARCH model for volatility estimation. Prerequisite: ARIMAX model for stationary time series. It is known that stock/bond/commodity price or currency rate in financial markets show a specific tendency in their volatility; while trending in a direction with moderate variance in bull or bear markets, they sometimes fluctute significantly. Smart traders use this kind of fluctuation as an important signal. Note: For more studies about volatility in financial markets, see. In other words,. ARCH break...
Logical Intuitions | Quantitative methods for intuitive understandings | Page 2
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Numerical differentiation is implemented for functions which is very hard or impossible to analytically express. Or, it is sometimes applied in the cases where the calculation is simply too hard. Continue reading Numerical Differentiation. Type: Lower bound / infinite / asymmetric / continuous. Number of Parameters: 2. Use: Alternative to lognormal distribution. Support: X [0, ). Parameters: 0 α, 0 β. If β 1, else undefined. Β 2, else undefined. Pdf and cdf of log-logistic distribution. Support: x [0, ).
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Logical Intuitions | Quantitative methods for intuitive understandings
Quantitative methods for intuitive understandings. Skip to primary content. Skip to secondary content. In statistical estimation or forecasting, when probability distribution of target variable is already known, then we don’t need to run MC and analytical ( true ) answer can be computed immediately. However, if it is unknown, or known yet too hard to analytically solve, then Monte-Carlo simulation is the only method to get an appropriate answer. This is more realistic case. Continue reading →. Among many...
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