may make sense to read the book’s footnote on this one…
The Modified IRR method differs from the original internal rate of return method in that the exponent is the proportion of the measurement period that each cash flow is in the portfolio. Therefore, while the original IRR is a money-weighted return, the Modified IRR approximates a time-weighted return.
so while the original IRR would measure e.g. period 1, 2, 3 and so on…
here wi would refer to the time period as 1/12 if monthly or say 15/365 if cash flow occurred on the 15th day of the first month.