A Closed-form Expression for the Variance of Truncated Distribution and its Uses
This work sheds some light on the relationship between a distribution's standard deviation and its range, a topic that has been discussed extensively in the literature. While many previous studies have proposed inequalities or relationships that depend on the shape of the population distributi...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Instituto Nacional de Estatística | Statistics Portugal
2025-08-01
|
| Series: | Revstat Statistical Journal |
| Subjects: | |
| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/625 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849243333610700800 |
|---|---|
| author | Roberto Vila Narayanaswamy Balakrishnan Raul Matsushita |
| author_facet | Roberto Vila Narayanaswamy Balakrishnan Raul Matsushita |
| author_sort | Roberto Vila |
| collection | DOAJ |
| description |
This work sheds some light on the relationship between a distribution's standard deviation and its range, a topic that has been discussed extensively in the literature. While many previous studies have proposed inequalities or relationships that depend on the shape of the population distribution, the approach here is built on a family of bounded probability distributions based on skewing functions. We offer closed-form expressions for its moments and the asymptotic behavior as the support's semi-range tends to zero and infinite. We also establish an inequality in which the well-known Popoviciu's one is a special case. Finally, we provide an example using US dollar prices in four different currencies traded on foreign exchange markets to illustrate the results developed here.
|
| format | Article |
| id | doaj-art-6fa0dd60690049f8afcdaa7300211381 |
| institution | Kabale University |
| issn | 1645-6726 2183-0371 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj-art-6fa0dd60690049f8afcdaa73002113812025-08-20T03:59:31ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712025-08-0123310.57805/revstat.v23i3.625A Closed-form Expression for the Variance of Truncated Distribution and its UsesRoberto Vila0https://orcid.org/0000-0003-1073-0114Narayanaswamy Balakrishnan 1https://orcid.org/0000-0001-5842-8892Raul Matsushita 2https://orcid.org/0000-0001-8864-6356University of BrasíliaMcMaster UniversityUniversity of Brasília This work sheds some light on the relationship between a distribution's standard deviation and its range, a topic that has been discussed extensively in the literature. While many previous studies have proposed inequalities or relationships that depend on the shape of the population distribution, the approach here is built on a family of bounded probability distributions based on skewing functions. We offer closed-form expressions for its moments and the asymptotic behavior as the support's semi-range tends to zero and infinite. We also establish an inequality in which the well-known Popoviciu's one is a special case. Finally, we provide an example using US dollar prices in four different currencies traded on foreign exchange markets to illustrate the results developed here. https://revstat.ine.pt/index.php/REVSTAT/article/view/625truncated distributionskewing functionPopoviciu's inequality |
| spellingShingle | Roberto Vila Narayanaswamy Balakrishnan Raul Matsushita A Closed-form Expression for the Variance of Truncated Distribution and its Uses Revstat Statistical Journal truncated distribution skewing function Popoviciu's inequality |
| title | A Closed-form Expression for the Variance of Truncated Distribution and its Uses |
| title_full | A Closed-form Expression for the Variance of Truncated Distribution and its Uses |
| title_fullStr | A Closed-form Expression for the Variance of Truncated Distribution and its Uses |
| title_full_unstemmed | A Closed-form Expression for the Variance of Truncated Distribution and its Uses |
| title_short | A Closed-form Expression for the Variance of Truncated Distribution and its Uses |
| title_sort | closed form expression for the variance of truncated distribution and its uses |
| topic | truncated distribution skewing function Popoviciu's inequality |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/625 |
| work_keys_str_mv | AT robertovila aclosedformexpressionforthevarianceoftruncateddistributionanditsuses AT narayanaswamybalakrishnan aclosedformexpressionforthevarianceoftruncateddistributionanditsuses AT raulmatsushita aclosedformexpressionforthevarianceoftruncateddistributionanditsuses AT robertovila closedformexpressionforthevarianceoftruncateddistributionanditsuses AT narayanaswamybalakrishnan closedformexpressionforthevarianceoftruncateddistributionanditsuses AT raulmatsushita closedformexpressionforthevarianceoftruncateddistributionanditsuses |