## Brazilian Journal of Probability and Statistics

- Braz. J. Probab. Stat.
- Volume 27, Number 4 (2013), 565-584.

### The complementary exponential power series distribution

José Flores D., Patrick Borges, Vicente G. Cancho, and Francisco Louzada

#### Abstract

In this paper, we introduce the complementary exponential power series distributions, with failure rate increasing, which is complementary to the exponential power series model proposed by Chahkandi and Ganjali [*Comput. Statist. Data Anal.* **53** (2009) 4433–4440]. The new class of distribution arises on latent complementary risks scenarios, where the lifetime associated with a particular risk is not observable, rather we observe only the maximum lifetime value among all risks. This new class contains several distributions as a particular case. The properties of the proposed distribution class are discussed, such as quantiles, moments and order statistics. Estimation is carried out via maximum likelihood. Simulation results on maximum likelihood estimation are presented. A real application illustrates the usefulness of the new distribution class.

#### Article information

**Source**

Braz. J. Probab. Stat., Volume 27, Number 4 (2013), 565-584.

**Dates**

First available in Project Euclid: 9 September 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.bjps/1378729988

**Digital Object Identifier**

doi:10.1214/11-BJPS182

**Mathematical Reviews number (MathSciNet)**

MR3105044

**Zentralblatt MATH identifier**

1298.62176

**Keywords**

Complementary risks exponential distribution increasing failure rate power series distribution exponential power series distribution

#### Citation

Flores D., José; Borges, Patrick; Cancho, Vicente G.; Louzada, Francisco. The complementary exponential power series distribution. Braz. J. Probab. Stat. 27 (2013), no. 4, 565--584. doi:10.1214/11-BJPS182. https://projecteuclid.org/euclid.bjps/1378729988