According to the Imperial Household Agency, the empress's final resting place is in an earthen tumulus ("kofun"). Jingū is venerated at a memorial Shinto shrine ("misasagi") at Nara.
In the centuries before the Meiji period, Jingū was known as the 15th Japanese imperial ruler, according to the traditional order of succession. However, Jingū's name is now removed from the official list of emperors of Japan. Jingū's son, Emperor Ōjin, is today considered to have been the 15th emperor in the order of succession.
Hypermodern
The hypermoderns were a school of chess players who set out to rethink some of the principles of chess openings. The name was given to them by the Polish-French grandmaster Tartakower.
The key idea was, in reaction to the older ideas of Siegbert Tarrasch, to dispute control of the centre by more subtle methods. Whereas old theory was to occupy the centre with two or three pawns immediately, the hypermoderns concentrated more on attacking the opponent's centre. A characteristic first move was 1Nf3 with White, or 1...Nf6 with Black, especially in reply to 1d4. To 1e4 they favoured an asymmetric defence such as 1...e6 or 1...c5 rather than the classical reply 1...e5.
Nimzovich was the founder, and Alekhine, Tartakower, Réti, Grünfeld, and Bogolyubov all took part. All were top grandmasters of the 1920s and 30s. Several modern openings owe their popularity to this group: Alekhine's Defence (1e4 Nf6); Réti's Opening (1Nf3); the King's Indian Defence (1d4 Nf6 2c4 g6 3Nc3 Bg7); the Grünfeld Defence (1d4 Bf6 2c4 g6 3Nc3 d5) and the Modern Defence (1...g6).
Confidence interval
In statistics, a confidence interval, abbreviated as CI, is a special interval for estimating a certain parameter, such as the population mean. With this method, a whole interval of acceptable values for the parameter is given instead of a single value—together with a likelihood that the real (unknown) value of the parameter will be in the interval. Thus, if we're not sure of the exact number of vehicles that crossed a bridge, we can say 400 plus or minus 10 instead of just saying 400.
The confidence interval is based on the observations from a sample, and hence differs from sample to sample. The likelihood that the parameter will be in the interval is called the confidence level, and the end points of the confidence interval are referred to as confidence limits.
Very often, this is given as a percentage (for example, the 95% confidence interval). The confidence interval is always given together with the confidence level. For a given estimation procedure in a given situation, the higher the confidence level, the wider the confidence interval will be.
The calculation of a confidence interval generally requires assumptions about the nature of the estimation process, since it is primarily a "parametric" method. One common assumption is that the distribution of the population from which the sample came is normal. As such, confidence intervals as discussed below are not robust statistics, though changes can be made to add robustness.
The term "confidence" has a similar meaning in statistics, as in common use. In common usage, a claim to 95% confidence in something is normally taken as indicating near certainty. In statistics, a claim to 95% confidence simply means that the researcher has seen one possible interval from a large number of possible ones, from which 19 out of 20 intervals contain the true value of the parameter.
A machine fills cups with margarine. It is adjusted so that the content of the cups is 250g of margarine. As the machine cannot fill every cup with exactly 250g, the content added to individual cups shows some variation, and is considered a random variable X.
This variation is assumed to be normally distributed around the desired average of 250g, with a standard deviation of 2.5g. To determine if the machine is adequately calibrated, a sample of "n" = 25 cups of margarine is chosen at random, and the cups are weighed. The weights of margarine are "X", ..., "X", a random sample from "X".
To get an impression of the expectation μ, an estimate is needed. The appropriate estimator is the sample mean:
The sample shows actual weights "x", ...,"x", with mean:
If we take another sample of 25 cups, we could easily expect to find values like 250.4 or 251.1 grams. A sample mean value of 280 grams, however, would be extremely rare if the mean content of the cups is in fact close to 250g.
There is a whole interval around the observed value 250.2 of the sample mean within which, if the whole population mean actually takes a value in this range, the observed data would not be considered particularly unusual. Such an interval is called a confidence interval for the parameter "μ".
To calculate such an interval, the endpoints of the interval have to be calculated from the sample, so they are statistics, functions of the sample "X", ..., "X", and hence are random variables themselves.
In our case, we may determine the endpoints by considering that the sample mean from a normally distributed sample is also normally distributed, with the same expectation "μ", but with standard error "σ"/√"n" = 0.5 (grams). By standardizing, we get a random variable
which depends on the parameter μ to be estimated, but with a standard normal distribution independent of the parameter "μ". Hence it is possible to find numbers −"z" and "z", independent of "μ", where "Z" lies in between with probability 1 − α, a measure of how confident we want to be. We take 1 - α = 0.95. So we have:
The number "z" follows from the cumulative distribution function:
and we get:
This might be interpreted as: with probability 0.95, we will find a confidence interval in which we will meet the parameter "μ" between the stochastic endpoints
and
This does not mean that there is 0.95 probability of meeting the parameter μ in the calculated interval. Every time the measurements are repeated, there will be another value for the mean of the sample. In 95% of the cases, "μ" will be between the endpoints calculated from this mean, but in 5% of the cases, it will not be. The actual confidence interval is calculated by entering the measured weights in the formula. Our 0.95 confidence interval becomes:
As the desired value 250 of "μ" is within the resulted confidence interval, there is no reason to believe the machine is wrongly calibrated.
The calculated interval has fixed endpoints, where μ might be in between (or not). Thus this event has probability either 0 or 1. We "cannot" say: "with probability (1 − α), the parameter "μ" lies in the confidence interval." We only know that by repetition in 100(1 − α) % of the cases, μ will be in the calculated interval. In 100α % of the cases, however, it does not. And unfortunately we do not know in which of the cases this happens. That is why we say: "with confidence level 100(1 − α) %, "μ" lies in the confidence interval."
The figure on the right shows 50 realisations of a confidence interval for a given population mean μ. If we randomly choose one realisation, the probability that it contains the parameter is 95%. However, it is also possible that we may have unluckily picked the wrong one as well.
Emperor Richū
Some scholars identify him with King San in the Book of Song. King San sent messengers to the Song Dynasty at least twice in 421 and 425; and this historical person was succeeded by his younger brother.
No certain dates can be assigned to this emperor's life or reign. The conventionally accepted names and sequence of the early emperors were not to be confirmed as "traditional" until the reign of Emperor Kammu, who was the 50th monarch of the Yamato dynasty.
According to "Nihonshoki" and "Kojiki", he was the first son of Emperor Nintoku.
Richū had two sons; but he was followed on the throne by his brother, who would become known as Emperor Hanzei. The enthronement of Hanzei by-passed Richū's two sons. Few other details have survived.