My research on the USDJPY's daily highs and lows has become very substantial. I've examined 509 days, from 7 Nov 2012 to yesterday (27 Oct 2014).
This is the distribution of the currency pair's daily highs and lows, sorted by hour. The distribution is heavily skewered towards the pre-Tokyo session, and the first few hours of the Tokyo session itself. The next significant cluster of daily highs and lows is around the European / US session overlap. I assume this is when the large Tokyo day positions are closed, taking advantage of the rush of liquidity from US and European customers.
The results of the table above is substantially different than the table in my previous entry, where I made a mathematical mistake (it's hard to explain - basically the table in my previous entry measured the distribution of daily highs and lows for each hour, rather than the probability of finding a daily high or low for each hour. For example, while the distribution of daily highs and lows should be roughly 50% for the first half of the day, and 50% for the later half of the day, the probability of finding a daily high or low in the first half of the day should be close to 100%. Likewise, the probability of finding a daily high or low in the later half of the day should be close to 100%).
How can we use this information? As mentioned in my previous post, if you're day-trading, opening a position in the first 4 hours of the day would seem to be your best bet. You can probably design a system on the 4H timeframe, entering on the break of the first 4H candle of the day, with your SL on the opposite end of the candle (there's an approx. ~58% chance that the opposite end will be the day's high or low). Where you set your reward - that's for you to find out. :)
My statistics maths is a little fuzzy, but I believe the table above is correct.