Probability density function

About: Probability density function is a research topic. Over the lifetime, 22321 publications have been published within this topic receiving 422885 citations. The topic is also known as: probability function & PDF.

A density-based indexing method for efficient execution of high-dimensional nearest-neighbor queries on large databases

Abstract: Method and apparatus for efficiently performing nearest neighbor queries on a database of records wherein each record has a large number of attributes by automatically extracting a multidimensional index from the data The method is based on first obtaining a statistical model of the content of the data in the form of a probability density function This density is then used to decide how data should be reorganized on disk for efficient nearest neighbor queries At query time, the model decides the order in which data should be scanned It also provides the means for evaluating the probability of correctness of the answer found so far in the partial scan of data determined by the model In this invention a clustering process is performed on the database to produce multiple data clusters Each cluster is characterized by a cluster model The set of clusters represent a probability density function in the form of a mixture model A new database of records is built having an augmented record format that contains the original record attributes and an additional record attribute containing a cluster number for each record based on the clustering step The cluster model uses a probability density function for each cluster so that the process of augmenting the attributes of each record is accomplished by evaluating each record's probability with respect to each cluster Once the augmented records are used to build a database the augmented attribute is used as an index into the database so that nearest neighbor query analysis can be very efficiently conducted using an indexed look up process As the database is queried, the probability density function is used to determine the order clusters or database pages are scanned The probability density function is also used to determine when scanning can stop because the nearest neighbor has been found with high probability

Logspline Density Estimation for Censored Data

Abstract: Logspline density estimation is developed for data that may be right censored, left censored, or interval censored. A fully automatic method, which involves the maximum likelihood method and may involve stepwise knot deletion and either the Akaike information criterion (AIC) or Bayesian information criterion (BIC), is used to determine the estimate. In solving the maximum likelihood equations, the Newton–Raphson method is augmented by occasional searches in the direction of steepest ascent. Also, a user interface based on S is described for obtaining estimates of the density function, distribution function, and quantile function and for generating a random sample from the fitted distribution.

Statistics of the occupation time of renewal processes

Abstract: We present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time. According to the nature of the distribution of time intervals, the probability density functions of these random variables have very different scalings in time. We analyze successively the cases where this distribution is narrow, where it is broad with index $\theta <1$, and finally where it is broad with index $1<\theta <2$. The methods introduced in this work provide a basis for the investigation of the statistics of the occupation time of more complex stochastic processes (see joint paper by G. De Smedt, C. Godr\`{e}che, and J.M. Luck).

Graphical Communication of Uncertain Quantities to Nontechnical People

Abstract: Nine pictorial displays for communicating quantitative information about the value of an uncertain quantity, x, were evaluated for their ability to communicate 2, p(x > a) and p( b > x > a) to well-educated semi- and nontechnical subjects. Different displays performed best in different applications. Cumulative distribution functions alone can severely mislead some subjects in estimating the mean. A “rusty” knowledge of statistics did not improve performance, and even people with a good basic knowledge of statistics did not perform as well as one would like. Until further experiments are performed, the authors recommend the use of a cumulative distribution function plotted directly above a probability density function with the same horizontal scale, and with the location of the mean clearly marked on both curves.