The Lognormal Distribution vs. the Normal Distribution
A variable X is said to have a lognormal distribution if Y = ln(X) is normally distributed, where “ln” denotes the natural logarithm. In other words, when the logarithms of values form a normal distribution, we say that the original…
Shortfall Risk, Safety-first Ratio and Selection of an Optimal Portfolio Using Roy’s Safety-first Criterion
Shortfall Risk Shortfall risk refers to the probability that a portfolio will not exceed the minimum (benchmark) return that has been set by an investor. In other words, it is the risk that a portfolio will fall short of the…
The Standard Normal Distribution: Calculation and Interpretation of Probability
The standard normal distribution refers to a normal distribution that has been standardized such that it has a mean of 0 and a standard deviation of 1. The shorthand notation used is:
Confidence Intervals
A confidence interval (CI) gives an “interval estimate” of an unknown population parameter such as the mean. It gives us the probability that the parameter lies within the stated interval (range). The precision or accuracy of the estimate depends on…
Univariate vs. Multivariate Distributions and the Role of Correlation in the Multivariate Normal Distribution
Univariate and multivariate normal distributions are very robust and useful in most statistical procedures. Understanding their form and function will help you learn a lot about most statistical routines.
Key Properties of the Normal Distribution
A random variable is said to have the normal distribution (Gaussian curve) if its values make a smooth curve that assumes a “bell shape.” A normal variable has a mean “μ,” pronounced as “mu,” and a standard deviation “σ,” pronounced…
Continuous Uniform Distribution
The continuous uniform distribution is such that the random variable X takes values between α (lower limit) and β (upper limit). In the field of statistics, α and β are known as the parameters of the continuous uniform distribution. We…
Functions and Definitions of Money
Definitions of Money According to Growther, money refers to anything that is generally accepted as a means of exchange. What’s more, it is that which at the same time acts as a measure and store of value. John Maynard Keynes…
Compare Monetary and Fiscal Policy
Monetary policy and fiscal policy refer to government policies and tools used to control macroeconomic variables and financial markets. Whenever economic activities start to slow down, these tools are used to accelerate growth. Similarly, when the economy starts to overheat,…
The Construction of Indices Used to Measure Inflation
Since inflation is impactful on the general price level of an economy, it is tantamount to measure inflation using a price index. As such, it is important to understand how a price index is modeled so that inflation rates derived…
