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A new family of compound lifetime distributions

A. Asgharzadeh, Hassan S. Bakouch, Saralees Nadarajah, L. Esmaeili (2014)

Kybernetika

In this paper, we introduce a general family of continuous lifetime distributions by compounding any continuous distribution and the Poisson-Lindley distribution. It is more flexible than several recently introduced lifetime distributions. The failure rate functions of our family can be increasing, decreasing, bathtub shaped and unimodal shaped. Several properties of this family are investigated including shape characteristics of the probability density, moments, order statistics, (reversed) residual...

A new family of trivariate proper quasi-copulas

Manuel Úbeda-Flores (2007)

Kybernetika

In this paper, we provide a new family of trivariate proper quasi-copulas. As an application, we show that W 3 – the best-possible lower bound for the set of trivariate quasi-copulas (and copulas) – is the limit member of this family, showing how the mass of W 3 is distributed on the plane x + y + z = 2 of [ 0 , 1 ] 3 in an easy manner, and providing the generalization of this result to n dimensions.

A new kind of augmentation of filtrations

Joseph Najnudel, Ashkan Nikeghbali (2011)

ESAIM: Probability and Statistics

Let (Ω, ℱ , ( ℱ t )t≥0, ℙ ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to ℱ ∞ (theσ-algebra generated by ( ℱ t )t≥0) a coherent family of probability measures ( ℚ t ) indexed byt≥0, each of them being defined on ℱ t . It is known that for instance, on the Wiener space, this extension problem has a positive answer if one takes the filtration generated by the coordinate process, made right-continuous, but can have a negative answer if one takes its usual augmentation....

A new kind of augmentation of filtrations

Joseph Najnudel, Ashkan Nikeghbali (2011)

ESAIM: Probability and Statistics

Let (Ω, ℱ , ( ℱ t )t≥0, ℙ ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to ℱ ∞ (the σ-algebra generated by ( ℱ t )t≥0) a coherent family of probability measures ( ℚ t ) indexed by t≥0, each of them being defined on ℱ t . It is known that for instance, on the Wiener space, this extension problem has a positive answer if one takes the filtration generated by the coordinate process, made right-continuous, but can have a negative answer if one takes its usual...

A new proof of Kellerer’s theorem

Francis Hirsch, Bernard Roynette (2012)

ESAIM: Probability and Statistics

In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.

A new proof of Kellerer’s theorem

Francis Hirsch, Bernard Roynette (2012)

ESAIM: Probability and Statistics

In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.

Currently displaying 341 – 360 of 10046