There are a number of factors that affect the battery life, and these are the chip itself, its firmware, the pcb design, error in the device's configuration, environmental temperature, the housing, and so on and so forth. First lets have a look at an ideal condition where the environment is perfect and predictable so that we can easily create formula at how the device can consume power. In a perfect environment we can easily say that Battery Life(in Days) = Transmission Rate(mSeconds) * Rated Transmission Count where Rated Transmission Count = Battery Rating(in mAH) / Current Draw per Transmission where Current Draw per Transmission = Power Consumption per Transmission(in dBm converted into µWatts) / Voltage.
1) Battery Rating = 260mAH
2) Device Rated Transmission Power = -23dBm = 3.33µW(AT+POWE3)
3) Transmission Rate = 564mseconds(AT+ADVI5)
3) Voltage Applied to the iBeacon = 3.3V
Current Draw per Transmission = 3.33 µW / 3.3V = 0.1 µA (assuming that 3.3v is constant)
Rated Transmission Count = 260 mAH / 0.1 µA = 2600000
Battery Life = 564mseconds * 2600000 / 86400 = 16.97 days
The ibeacon consumes 0.18mA during sleep mode, to compute the battery life:
Total Transmission Current Draw Per Hour = 0.1 µA * 564mseconds * 3600 = 0.203mA
Using the formula from digikey:
Net Battery Life = (((260 mAH / (0.18 mA+0.203mA)) * 0.7)/24 = 13.86 days(estimate only)
Please note that Battery Rating in mAH is not actually the amount of electrical energy stored by the battery, it is the maximum current that can be drawn from the battery continuously in one hour. So we will just assume that the battery has already been fully discharged after an hour of giving off 260mA.
These formulae is based on perfect conditions, but because of some other factors that I enumerated above, these result could vary by as much as 50%(with the exception of the error in the device's configuration that could result up to 1000%)when all other factors are considered in the calculation.
I could not site a reputable link that there was indeed a scientific study to confirm my observation, it was based solely on my actual experience with electronic devices that I have worked on the past 5 years.