Secretary problem with vanishing objects

We consider a version of the secretary problem where elements may vanish during the selection and become unchoosable. We construct a selection strategy and identify the probability to select the best element, which turns out to be asymptotically maximal as number of elements increases indefinitely. As an auxiliary result of independent interest we establish large deviation probability estimates for sums of independent variables with distinct geometric distribution.

TIME SERIES ANALYSIS AND FORECAST ESTIMATES FOR THE MEAN ANNUAL RIVERINE WATER RUNOFF WITHIN THE UKRAINIAN PART OF THE PRUT AND SIRET BASINS

The systematization, generalization, estimation of the variability of time series of the mean annual water runoff of rivers in of the Prut and Siret basins has been carried out, and its cyclic structure has been revealed. For this purpose, a database of average annual discharges water with 12 of hydrological observing stations on the rivers in of the Prut and Siret basins from the beginning of observations to 2015 have been created. Number of years under observation by the annual runoff values for river Prut near city of Chernivtsi is 121. Their representativeness and homogeneity for practical calculations has been evaluated. To identify and formalize the cyclic structure of time series of the mean annual water runoff of rivers in of the Prut and Siret basins used the methods of mathematical statistics and theory of random functions: a function of mathematical expected value; a function of dispersion values or standard deviation; probability distribution function; autocorrelation function. Also have been involved different of the standard mathematical criteria (criteria homogeneity, criteria of the series and of the longest series), integral curves of the differences. As a result, the structure of cyclic oscillations is revealed of the mean annual water runoff of rivers in the Prut and Siret basins and that is what made it possible to provide forecast estimates until 2050.

Optimal leverage ratio estimate of various models for leveraged ETFs to exceed a target: Probability estimates of large deviations

In this paper, we study the deviation probability estimate for a leveraged exchanged-traded fund (LETF). By large deviation principle, we derive explicitly the logarithmic limit of the tail probability when the price of a LETF exceeds a given reference asset, which allows us to compute the underlying leverage ratio. Then we apply our results to various existing models, including the geometric Brownian motion (GBM) model, generalized autoregressive conditional heteroskedasticity (GARCH) model, inverse GARCH model, extended Cox–Ingersoll–Ross (CIR) model, 3/2 model, as well as the Heston and 3/2 stochastic volatility models, and to present their corresponding optimal leverage ratios, respectively.

Fuzzy based binary feature profiling for modus operandi analysis

It is a well-known fact that some criminals follow perpetual methods of operations known as modi operandi. Modus operandi is a commonly used term to describe the habits in committing crimes. These modi operandi are used in relating criminals to crimes for which the suspects have not yet been recognized. This paper presents the design, implementation and evaluation of a new method to find connections between crimes and criminals using modi operandi. The method involves generating a feature matrix for a particular criminal based on the flow of events of his/her previous convictions. Then, based on the feature matrix, two representative modi operandi are generated: complete modus operandi and dynamic modus operandi. These two representative modi operandi are compared with the flow of events of the crime at hand, in order to generate two other outputs: completeness probability (CP) and deviation probability (DP). CP and DP are used as inputs to a fuzzy inference system to generate a score which is used in providing a measurement for the similarity between the suspect and the crime at hand. The method was evaluated using actual crime data and ten other open data sets. In addition, comparison with nine other classification algorithms showed that the proposed method performs competitively with other related methods proving that the performance of the new method is at an acceptable level.

Fuzzy based binary feature profiling for modus operandi analysis

It is a well-known fact that some criminals follow perpetual methods of operations, known as modus operandi (MO) which is commonly used to describe the habits in committing something especially in the context of criminal investigations. These modus operandi are then used in relating criminals to other crimes where the suspect has not yet been recognized. This paper presents a method which is focused on identifying the perpetual modus operandi of criminals by analyzing their previous convictions. The method involves in generating a feature matrix for a particular suspect based on the flow of events. Then, based on the feature matrix, two representative modus operandi are generated: complete modus operandi and dynamic modus operandi. These two representative modus operandi will be compared with the flow of events of the crime in order to investigate and relate a particular criminal. This comparison uses several operations to generate two other outputs: completeness probability and deviation probability. These two outcomes are used as inputs to a fuzzy inference system to generate a score value which is used in providing a measurement for the similarity between the suspect and the crime at hand. The method was evaluated using actual crime data and four other open data sets. Then ROC analysis was performed to justify the validity and the generalizability of the proposed method. In addition, comparison with five other classification algorithms showed that the proposed method performs competitively with other related methods.

Fuzzy based binary feature profiling for modus operandi analysis

It is a well-known fact that some criminals follow perpetual methods of operations, known as modus operandi (MO) which is commonly used to describe the habits in committing something especially in the context of criminal investigations. These modus operandi are then used in relating criminals to other crimes where the suspect has not yet been recognized. This paper presents a method which is focused on identifying the perpetual modus operandi of criminals by analyzing their previous convictions. The method involves in generating a feature matrix for a particular suspect based on the flow of events. Then, based on the feature matrix, two representative modus operandi are generated: complete modus operandi and dynamic modus operandi. These two representative modus operandi will be compared with the flow of events of the crime in order to investigate and relate a particular criminal. This comparison uses several operations to generate two other outputs: completeness probability and deviation probability. These two outcomes are used as inputs to a fuzzy inference system to generate a score value which is used in providing a measurement for the similarity between the suspect and the crime at hand. The method was evaluated using actual crime data and four other open data sets. Then ROC analysis was performed to justify the validity and the generalizability of the proposed method. In addition, comparison with five other classification algorithms showed that the proposed method performs competitively with other related methods.