Math and Statistics
Mathematical essentials for the finance world
What is the relative standard error?
In statistics, a relative standard error (RSE) is equal to the standard error of a survey estimate divided by the survey estimate and then multiplied by 100. The number is multiplied by 100 so it can be expressed as a percentage. The RSE does not necessarily represent any new information beyond the standard error, but it might be a superior method of presenting statistical confidence. Standard error measures how much a survey estimate is likely to deviate from the actual population. By contrast, relative standard error (RSE) is the standard error expressed as a fraction of the estimate and is usually displayed as a percentage.
How do odds work in casino and sports betting?
If you are planning to enter the betting world, it is important to be able to understand and interpret all types of odds well. You need to be familiar with the conversions between the different formats of odds, the conversion of odds into implied probabilities, and the differences between the true chances of an outcome, as well as the odds on display. The three main types of betting odds are fractional (British) odds, decimal (European) odds, and moneyline (American) odds. These types are alternate ways of presenting the same thing and hold no difference in terms of payouts.
What do I apply the geometric mean?
In statistics, the geometric mean is calculated by raising the product of a series of numbers to the inverse of the total length of the series. The geometric mean is most useful when numbers in the series are not independent of each other or if numbers tend to make large fluctuations. Applications of the geometric mean are most common in business and finance, where it is frequently used when dealing with percentages to calculate growth rates and returns on a portfolio of securities. It is also used in certain financial and stock market indexes.
When is it better to use systematic over simple random sampling?
Systematic sampling is easier to execute than simple random sampling, and it can produce skewed results if the data set exhibits patterns. It is also more easily manipulated. Meanwhile, systematic sampling chooses a data point per each predetermined interval. On the contrary, simple random sampling is best used for smaller data sets and can produce more representative results. In simple random sampling, each data point has an equal probability of being chosen.
What’s the difference between positive and inverse correlation?
A positive correlation is evident when two variables move in the same direction. When the strength of the correlation is measured, a positive correlation will be a positive number.
An inverse correlation is evident when two variables move in the opposite direction and will be a negative number and then strength of the correlation is measured. Investors who want to hedge against risk often seek out stocks in sectors that have a negative price correlation with their other investments. Correlation can be accidental. Investors look for rational reasons why one sector moves in tandem with another sector or in the opposite direction. That makes it more likely that the correlation will occur consistently.
A Poisson distribution can be used to estimate how many times an event is likely to occur within "X" periods of time. Poisson distributions are used when the variable of interest is a discrete count variable. Many economic and financial data appear as count variables, such as how many times a person becomes unemployed in a given year, thus lending themselves to analysis with a Poisson distribution.
Boolean algebra is a branch of mathematics that deals with operations on logical values with binary variables. Boolean algebra utilizes conjunction, disjunction, and negation, as opposed to addition, subtraction, multiplication, and division. The primary modern use of Boolean algebra is in computer programming languages. In finance, Boolean algebra is used in binomial options pricing models, which helps determine when an option should be exercised.
Type 1 Error
A type I error occurs during hypothesis testing when a null hypothesis is rejected, even though it is accurate and should not be rejected. The null hypothesis assumes no cause and effect relationship between the tested item and the stimuli applied during the test. A type I error is "false positive" leading to an incorrect rejection of the null hypothesis.
Both linear and nonlinear regression predict Y responses from an X variable (or variables). Nonlinear regression is a curved function of an X variable (or variables) that is used to predict a Y variable. Nonlinear regression can show a prediction of population growth over time.
Homoskedasticity occurs when the variance of the error term in a regression model is constant. If the variance of the error term is homoskedastic, the model was well-defined. If there is too much variance, the model may not be defined well. Adding additional predictor variables can help explain the performance of the dependent variable.
Prior probability, in Bayesian statistical inference, is the probability of an event before new data is collected. This is the best rational assessment of the probability of an outcome based on the current knowledge before an experiment is performed. The prior probability of an event will be revised as new data or information becomes available, to produce a more accurate measure of a potential outcome.