Distribution Name: Lognormal
Parameters:
- UB (Upper bound)
- LB (Lower bound)
Note that LB and UB in the Excel formula below represent a 90% CI. There is a 5% chance of being above the UB and a 5% chance of being below the LB.
The lognormal distribution is an often preferred alternative to the normal distribution when a sample can only take positive values. Consider the expected future value of a stock price. In the equation S1 = S0e(r), S1 is the future stock price, S0 is the present stock price, and r is the expected rate of return. The expected rate of return follows a normal distribution and may very well take a negative value. The future price of a stock, however, is bounded at zero. By taking the exponent of the normally distributed expected rate of return, we will generate a lognormal distribution where a negative rate may have an adverse effect on the future stock price, without ever leading the stock price below the zero bound. It also allows...