Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

(1966). Mathematical Theory of Reliability. Journal of the Operational Research Society: Vol. 17, No. 2, pp. 213-215.

https://link.springer.com/content/pdf/10.1057%2Fjors.1966.43.pdf

Mathematical Theory of Reliability

Dependence modeling with copulas

The extropy has recently been introduced as the dual concept of entropy. Moreover, in the context of the Dempster–Shafer evidence theory, Deng studied a new measure of discrimination, named the Deng entropy. In this paper, we define the Deng extropy and study its relation with Deng entropy, and examples are proposed in order to compare them. The behaviour of Deng extropy is studied under changes of focal elements. A characterization result is given for the maximum Deng extropy and, finally, a numerical example in pattern recognition is discussed in order to highlight the relevance of the new measure.

https://www.mdpi.com/1099-4300/22/5/582/pdf

A Dual Measure of Uncertainty: The Deng Extropy.

A unified formulation of entropy and its application

The cumulative entropy is an information measure which is alternative to the differential entropy. Indeed, the cumulative entropy of a random lifetime X can be expressed as the expectation of its mean inactivity time evaluated at X . In this paper we propose a new generalized cumulative entropy based on Tsallis entropy (CTE) and its dynamic version (DCTE). We study some properties and characterization results for this measure.

Some properties of cumulative Tsallis entropy

In this paper we present ROC methodology and analyze the ROC curve. We describe first the historical background and its relation with signal detection theory. Some mathematical properties of this curve are given, and in particular the relation with stochastic orders and statistical hypotheses testing are described. We present also a medical application of the Neymann–Pearson lemma.

Some mathematical properties of the ROC curve and their applications

The Shannon entropy based on the probability density function is a key information measure with applications in different areas. Some alternative information measures have been proposed in the literature. Two relevant ones are the cumulative residual entropy (based on the survival function) and the cumulative past entropy (based on the distribution function). Recently, some extensions of these measures have been proposed. Here, we obtain some properties for the generalized cumulative past entropy. In particular, we prove that it determines the underlying distribution. We also study this measure in coherent systems and a closely related generalized past cumulative Kerridge inaccuracy measure.

Properties for generalized cumulative past measures of information

Inactivity times of coherent systems with dependent components under periodical inspections

In this paper, a family of mean past weighted ($$\hbox {MPW}_{\alpha }$$) distributions of order $$\alpha $$ is introduced. For the construction of this family, the concepts of the mean inactivity time and cumulative $$\alpha $$-class past entropy are used. Distributional properties and stochastic comparisons with other known weighted distributions are given. Furthermore, an upper bound for the k-order moment of the random variables associated with the new family and a characterization result are obtained. Generalized discrete mixtures that involve $$\hbox {MPW}_{\alpha }$$ distributions and other weighted distributions are also explored.

Camilla Calì

Papers

Some properties of cumulative Tsallis entropy

Some mathematical properties of the ROC curve and their applications

Properties for generalized cumulative past measures of information

Inactivity times of coherent systems with dependent components under periodical inspections

A family of weighted distributions based on the mean inactivity time and cumulative past entropies