Trying to fit a Paranormal Distribution. LOL.

Guess what's the function to fit the above Paranormal Distribution. LOL.

What Usually The Fitted Curves Tries to Say. LOL.

Value at Risk's Formula At a Glance

Eddy said: A summary of some prominent approaches to VAR. There are more out there. Basically VAR approaches can be broadly classified into 2 types: Local Valuation and Full Valuation. Full Valuation VAR includes Monte Carlo and Historical Simulation whereas Local Valuation covers Factors Methods and Diagonal Methods.

Linear VAR, Full Valuation VAR, Delta VAR, Delta-Normal VAR, Delta-Gamma VAR, Monte Carlo VAR, Historical Simulation VAR.

Sir, a sample please?

If ever we got unlimited monies, processing powers, complete coverages and assuming no constraints at all, we can ignore the idea of sampling since by then doing sampling is like perfoming double works if we can actually work on the population itself.

Down to earth, in every business decision we faced the quintessential requirements to take some trade-offs between many constraints, i.e. budget and time. When deciding on business directions, strategy or even a daily routine task, it is imperative that the person to understand the nature of the problem before formulating a proper solution. To understand the problem in context, usually it involves actions such as monitoring certain characteristics of items, obtaining input from people and etc. If we can do the data gathering on every single item of interest, then we are working directly on the population instead of sampling part of it. Some problems mandate sampling because it is impractical to deal with entire population, if ever it is possible. For example, to find out the average height/weight of asian adult male, it is time consuming and might be impossible to capture the height information from every matched candidates. It may be the case that some of them are hiding somewhere in the jungle and therefore your data is incomplete. In other words, at best efforts, you are only approximating the population, i.e. sampling. Other sampling scenarios include production process control mechanism that check the product characteristics randomly at certain intervals, market research surveys that targeting certain stratum of some geographical locations and anthopological studies.

We now know that a sample is a subset or part of a population and a sampling process is basically drawing that part from that population. By having a representative, non-biased and sufficient sample, we could draw (i.e. infer) conclusions about the underlying population.

In the statement above, it is obvious that the conclusion might be misleading or totally wrong if the sample is "non-representative", "biased" and "insufficient".

So that's why some more complicated sampling techniques other than simple random sampling exists to reduce the effects of some of these, e.g. stratified sampling, cluster sampling and multistep sampling. But for you, just need to remember that all these techniques are just ways to draw items from the population.

Once you have a good sample, the next logical step you might want to perform includes organizing, describing and summarizing the samples quantitatively and graphically. The important milestone in this step is to get a grasp of the sample's probability distribution, i.e. the random variation pattern in the sample. From the probability distribution, you can infer about the population probability distribution. Only by confirming the distribution, you can be sure that your choice of analysis tools are compliant and consistent.

In terms of formal terms, statisticians use the word "statistic" for numerical characteristics of sample and the word "parameter" for similar characteristic of population. The common symbols used are different too, e.g. lowercase s for sample's standard deviation and lowercase greek letter sigma for population's standard deviation.

Some common probability distributions include hypergeometric, binomial and Poisson for discrete random variables and exponential and normal for continous randon variables, among others.

Well, all the above are fundamental knowledge, I'm just put it down in words. Easy right?

Multiplication Tricks

You don't really want to use this way to do multiplications involving number 5 or above, that is darn lots of lines to draw :p

Regression Model Specification Principles

Model specification refers to the set of variables included in the regression and the regression equation's functional form. The principles below cal guide model specification:

• The model should be grounded in cogent economic reasoning


• The functional form chosen for each variable in the regression should be appropriate given the nature of the variables


• The model should be parsimonious


• Validate the regression model assumptions before accepting them


• Apply the model using out-of-sample observations

F-Statistic

RSS is the Regression Sum of Squared
SSE is the Sum of Squared Error
n is the total number of observations
k is the number of independent variables in the regression equation

k and [n - ( k + 1)] is the number of degree of freedom for calculating a F-statistic.

For unbiased MSE calculation, the number of regression coefficients need to be substracted from the n to form the number of degree of freedom for the denominator.

In my understanding, F-statistic aims to highlight the ratio of explained variation to unexplained variation for the regression equation.

The basic concept is roughly like this: Assuming the absence of such regression equation in estimating the value of a dependent variable, let say Y. We probably will use the arithmetic average, denoted Y-bar to estimate the value of Y. In other word, in such cases, all of the variations would be unexplained, which means you can't really tell what factors that causes your prediction deviates from the actual.

So now, some smart ass come out with an equation that claims to be a better estimation method than arithmetic average. Ideally, the RSS will be larger than SSE because now the regression cofficients in the equation would partially (might be fully) explains the deviation from the actual.

If the equation performs as good (as worse) as the arithmetic mean method, then F-statistic would give you a 0 value because RSS will be zero.

Classic Linear Regression Assumptions

The assumptions of the classic linear regression model are the following:

1. A linear regression exists between the dependent variable and the independent variable.


2. The independent variable is not random.


3. The expected value of the error term is 0.


4. The variance for the error term is the same for all observations. (Homoskedasticity)


5. The error term is normally distributed.


6. The error term is uncorrelated across observations.

Practice more, then you will learn :)

Central Limit Theorem

Everybody should know Central Limit Theorem. You know right?

Basically, Central Limit Therom states that:

• The sampling distribution of the sample mean from a random sample representing the underlying population regardless of the population distribution is approximately normal.


• The mean for such sampling distribution is the population mean.


• The variance for such sampling distribution is the population variance divided by the sample size n.

A good mnemonic device to help remember the Central Limit Theorem is X ~ N(miu, sigma-squared/n). Literally it means X, the sample mean is a random variable that has an approximate normal distribution N that can be fully described by two characteristics, miu (the population mean) and sigma-squared/n (the squared of the population standard deviation divided by the sample size).

One of the utility of Central Limit Theorem is to help you establish a framework when estimating population parameters using sample statistics.

Richter Scale

Earthquake Intensity

The Richter scale is commonly used to measure the intensity of an earthquake. There are many different ways of computing this based on a variety of different quantities. We are going to take a quick look at the formula that uses the energy released during an earthquake.


If E is the energy released, measured in joules, during an earthquake then the magnitude of the earthquake is given by,



where
joules.