On a characterization of exponential, Pearson and Pareto distributions via covariance and pseudo-covariance

• Autorzy: Pawlas Piotr , Szynal Dominik

Identyfikatory

DOI

10.1515/dema-2020-0026

• Języki publikacji: EN

Abstrakty

EN

Properties of linear regression of order statistics and their functions are usually utilized for the characterization of distributions. In this paper, based on such statistics, the concept of Pearson covariance and the pseudo-covariance measure of dependence is used to characterize the exponential, Pearson and Pareto distributions.

Słowa kluczowe

EN

characterization; order statistics; linear regression; covariance; pseudo-covariance; uniform distribution; exponential distribution; Pearson type I distribution; Pareto distribution of second kind

PL

charakteryzacja; statystyki pozycyjne; regresja liniowa; kowariancja; rozkład jednostajny; rozkład wykładniczy; rozkłady Pearsona

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2020
• Tom: Vol. 53, nr 1
• Strony: 285--291
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Pawlas Piotr

• Institute of Mathematics, Maria Curie–Skłodowska University, Pl. M.Curie–Skłodowskiej 1, 20-031 Lublin, Poland

autor

Szynal Dominik

• Institute of Mathematics, Maria Curie–Skłodowska University, Pl. M.Curie–Skłodowskiej 1, 20-031 Lublin, Poland

Bibliografia

• [1] A. C. Dallas, A characterization of the exponential distribution, Bull. Soc. Math. Grèce14(1973), 172–175.
• [2] Y. H. Wang and R. C. Shrivastava, A characterization of the exponential and related distributions by linear regression, Ann. Statist. 8(1980), 217–220.
• [3] H. N. Nagaraja and V. B. Nevzorov, On characterizations based on record values and order statistics, J. Statist. Plann. Inference 63(1997), 271–284.
• [4] A. Dębińska and J. Wesołowski, Linearity of prediction for non-adjacent record values, J. Statist. Plann. Inference 90(2000), 195–200
• [5] M. Bieniek and D. Szynal, Characterizations based on k-th record values, Demonstr. Math. 37(2004), no. 2, 463–473.
• [6] P. Pawlas and D. Szynal, On a new measure of dependence and its applications, Demonstr. Math. 45(2012), no. 1, 243–256.
• [7] J. W. H. Swanepoel, A note on the characterization of the exponential distribution by the covariance of spacings, South African Statist. J. 25(1991), no. 2, 73–78.
• [8] P. Pawlas and D. Szynal, On a characterization of a power distribution, Demonstr. Math. 48(2014), no. 1, 100–106.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).