Suchergebnisse

Let {(Xi ,Yi), i ≥ 1} be independent and identically distributed random variables (RVs) from a continuous bivariate distribution. If {Rn,n ≥ 1} is the sequence of upper record values in the sequence {Xi}, then the RV Yi, which corresponds to Rn is called the concomitant of the nth record, denoted by R[n]. We study the Shannon entropy (SHANE) of R[n] and (Rn,R[n]) under iterated Farlie-Gumbel-Morgenstern (IFGM) family. In addition, we find the Kullback-Leibler distance (K-L) between R[n] and Rn. Moreover, we study the Fisher information matrix (FIM) for record values and their concomitants about the shape-parameter vector of the IFGM family. Also, we study the relative efficiency matrix of that vector-estimator of the shape-parameter vector whose covariance matrix is equal to Cramer-Rao lower bound, based on record ´ values and their concomitants. In addition, the Fisher information number (FIN) of R[n] is derived. Finally, we evaluate the FI about the mean of exponential distribution in the concomitants of record values.

This paper investigates the existence of multiple positive solutions for a class of φ−Laplacian boundary value problem with a nonlinear fractional differential equation and fractional boundary conditions. Multiple solutions are proved under slight conditions on a possibly degenerating source term. Approximation techniques together with the fixed-point index theory a on cone of a Banach space are employed. Some illustrating examples of are also supplied.
Mathematics Subject Classification (2010): 34A08, 34B15, 34B18, 47H10.
Received 27 July; Accepted 13 December 2021