we investigate the long-term behavior of solutions of the difference equation[ x_{n+1}=x_{n}x_{n-3}-1 ,, n=0 ,, 1 ,, ldots ,, ]noindent where the initial conditions $x_{-3} ,, x_{-2} ,, x_{-1} ,, x_{0}$ are real numbers.  in particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.

For a reversible and ergodic Markov chain {Xn, n ≥ 0} with invariant distribution π, we show that a valid confidence interval for π(h) can be constructed whenever the asymptotic variance σ P (h) is finite and positive. We do not impose any additional condition on the convergence rate of the Markov chain. The confidence interval is derived using the so-called fixed-b lag-window estimator of σ P ...

In recent years, more robust methods 'of estimating the size of a closed population (N) from capture-recapturedata have been developed. However, interval estimation for N has seen few practical developments. The usual approach for constructing a confidence interval, known as a Wahl confidence interval, is based on the assumption of asymptotic normality. It is well bown that the small sample dis...

Few studies have considered the functional relationship model for circular variables. Anuar has proposed a new of Circular Simultaneous Functional Relationship Model equal variances. However, confidence interval all parameter estimates in this not received any consideration literature. This paper proposes von Mises distribution model. The parameters are estimated using minimum sum (ms) and poly...

We construct an asymptotic confidence interval for the mean of a class of nonstationary processes with constant mean and time-varying variances. Due to the large number of unknown parameters, traditional approaches based on consistent estimation of the limiting variance of sample mean through moving block or non-overlapping block methods are not applicable. Under a block-wise asymptotically equ...