Abstract: The present invention describes a computer-based method comprising representing transactions involving assets that share a common characteristic, as respective data points associated with values of the assets, the data points including transaction value information, determining parameters that fit probability density functions to at least one component of a value spectrum of the data points, the probability density function for at least one of the components comprising a power law, the parameters not including an offset parameter representing possible shifts in the value spectrum over time, and forming an index of values associated with the assets using at least one of the determined parameters.

Abstract: Transactions involving assets that share a common characteristic are represented as respective data points associated with values of the assets. The data points include transaction value information. The data points belong to sets associated with respective geographical areas. Data points of at least two of the sets are aggregated into a superset representing transactions of a larger geographical region. A hypothetical probability density function is represented by a parametrization that describes the data points of the superset. An index is formed of values associated with the assets using at least one of the determined parameters.

Abstract: Transactions involving assets that share a common characteristic are represented as respective data points associated with values of the assets. The data points include transaction value information. Respective statistical values are determined for the data points with respect to a probability density function that fits a power law parameterization to the data points. A probability function describing the statistical values is evaluated as a measure of confidence that the probability density function of the data points is validly represented by the power law parametrization.

Abstract: Transactions involving assets that share a common characteristic are represented as respective data points associated with values of the assets, the data points including transaction value information, the data points theoretically excluding data points that are outside defined cutoffs, the cutoffs being defined so that effectively no data points are excluded at either a lower end, an upper end, or both. Parameters are determined that fit probability density functions to at least one component of a value spectrum of the data points, the probability density function for at least one of the components comprising a power law, the parameters not including an offset parameter representing possible shifts in the value spectrum over time. An index of values associated with the assets is formed using at least one of the determined parameters.

Abstract: Among other things, transactions involving assets that share a common characteristic are represented as respective data points associated with values of the assets, the data points including transaction value information. Parameters that fit probability distribution functions to at least two respective components of a value spectrum of the data points are determined. The probability distribution function for at least one of the components comprises a power law. An index is formed of values associated with the assets using at least one of the determined parameters.

Abstract: Among other things, transactions involving assets (for example, real estate assets) that share a common characteristic are represented as respective data points associated with values of the assets, the data points including transaction value information. Parameters are determined that fit probability density functions to at least one component of a value spectrum of the data points. The probability density function for at least one of the components comprises a power law. The parameters do not include an offset parameter representing possible shifts in the value spectrum over time. An index is formed of values associated with the assets using at least one of the determined parameters. The parameters may include at least one shape parameter determined by fitting data over multiple days and at least one position parameter determined by fitting data either over a single day or multiple days, the probability density function for at least one of the components comprising a power law.

Abstract: Transactions involving assets that share a common characteristic are represented as respective data points associated with values of the assets, the data points including transaction value information, the data points theoretically excluding data points that are outside defined cutoffs, the cutoffs being defined so that effectively no data points are excluded at either a lower end, an upper end, or both. Parameters are determined that fit probability density functions to at least one component of a value spectrum of the data points, the probability density function for at least one of the components comprising a power law, the parameters not including an offset parameter representing possible shifts in the value spectrum over time. An index of values associated with the assets is formed using at least one of the determined parameters.

Abstract: Transactions involving assets that share a common characteristic are represented as respective data points associated with values of the assets, the data points including transaction value information, the data points theoretically excluding data points that are outside defined cutoffs, the cutoffs being defined so that effectively no data points are excluded at either a lower end, an upper end, or both. Parameters are determined that fit probability density functions to at least one component of a value spectrum of the data points, the probability density function for at least one of the components comprising a power law, the parameters not including an offset parameter representing possible shifts in the value spectrum over time. An index of values associated with the assets is formed using at least one of the determined parameters.

Abstract: Among other things, transactions involving assets (for example, real estate assets) that share a common characteristic are represented as respective data points associated with values of the assets, the data points including transaction value information. Parameters are determined that fit probability density functions to at least one component of a value spectrum of the data points. The probability density function for at least one of the components comprises a power law. The parameters do not include an offset parameter representing possible shifts in the value spectrum over time. An index is formed of values associated with the assets using at least one of the determined parameters. The parameters may include at least one shape parameter determined by fitting data over multiple days and at least one position parameter determined by fitting data either over a single day or multiple days, the probability density function for at least one of the components comprising a power law.

Abstract: Among other things, transactions involving assets that share a common characteristic are represented as respective data points associated with values of the assets, the data points including transaction value information. Parameters that fit probability distribution functions to at least two respective components of a value spectrum of the data points are determined. The probability distribution function for at least one of the components comprises a power law. An index is formed of values associated with the assets using at least one of the determined parameters.

Abstract: Transactions involving assets that share a common characteristic are represented as respective data points associated with values of the assets. The data points include transaction value information. Respective statistical values are determined for the data points with respect to a probability density function that fits a power law parameterization to the data points. A probability function describing the statistical values is evaluated as a measure of confidence that the probability density function of the data points is validly represented by the power law parametrization.

Abstract: Transactions involving assets that share a common characteristic are represented as respective data points associated with values of the assets. The data points include transaction value information. The data points belong to sets associated with respective geographical areas. Data points of at least two of the sets are aggregated into a superset representing transactions of a larger geographical region. A hypothetical probability density function is represented by a parametrization that describes the data points of the superset. An index is formed of values associated with the assets using at least one of the determined parameters.

Abstract: A method of determining a path of an autonomous entity through an environment, the method comprising providing a provisional path through a model of the environment from a current location to an intended destination, providing a profile for said autonomous entity, determining a preferred step towards said intended destination based upon said profile and said provisional path, determining a personal space around said autonomous entity and determining whether said preferred step is feasible by considering whether obstructions infringe said personal space.

Abstract: A method of simulating movement of an autonomous entity through an environment, the method comprising providing a provisional path through a model of the environment from a current location to an intended destination, providing a profile for said autonomous entity, determining a preferred step towards said intended destination based upon said profile and said provisional path, determining a personal space around said autonomous entity and determining whether said preferred step is feasible by considering whether obstructions infringe said personal space.

Abstract: A method of determining a path of an autonomous entity through an environment, the method comprising providing a provisional path through a model of the environment from a current location to an intended destination, providing a profile for said autonomous entity, determining a preferred step towards said intended destination based upon said profile and said provisional path, determining a personal space around said autonomous entity and determining whether said preferred step is feasible by considering whether obstructions infringe said personal space.

Abstract: A method of simulating movement of an autonomous entity through an environment, the method comprising providing a provisional path through a model of the environment from a current location to an intended destination, providing a profile for said autonomous entity, determining a preferred step towards said intended destination based upon said profile and said provisional path, determining a personal space around said autonomous entity and determining whether said preferred step is feasible by considering whether obstructions infringe said personal space.