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In [[computing]], the '''alias method''' is a family of efficient [[algorithm]]s for [[pseudo-random number sampling|sampling from a discrete probability distribution]], due to A. J. Walker.<ref>A. J. Walker, Electronics Letters 10, 127 (1974); ACM TOMS 3, 253 (1977)</ref> The algorithms typically use <math>O(n \log n)</math> or <math>O(n)</math> preprocessing time, after which random values can be drawn from the distribution in <math>O(1)</math> time.<ref>Vose, Michael. [http://web.eecs.utk.edu/~vose/Publications/random.pdf A Linear Algorithm For Generating Random Numbers with a Given Distribution]</ref>


Internally, the algorithm builds two tables, a ''[[probability]] [[Table (information)|table]]'' and an ''alias table''. To generate a random outcome, a fair [[dice|die]] is rolled to determine an index into the probability table. Based on the probability stored at that index, a [[biased coin]] is then flipped, and the outcome of the flip is used to determine which result to output.<ref>[http://www.keithschwarz.com/darts-dice-coins/ Darts, Dice, and Coins: Sampling from a Discrete Distribution]. KeithSchwarz.com. Retrieved on 2011-12-27.</ref>


Potential buyers of Lancel see reviving the loss-making leather goods maker as a high-risk gamble that could take at least six or eight years to pay off, sources close to the matter say.<br><br>Facing a struggle to offload the business, Swiss parent Richemont (CFR.VX) would be ready to pay for two years of losses - up to an estimated 20 million euros ($28 million) - to entice bidders, the sources say.<br><br>So far private equity firms Change Capital and Lion Capital have expressed interest while Asian group Swire is looking to team up with a private equity firm to make a bid, according to the sources.<br>Another potential buyer, who has not made up his mind yet, is Jacques Veyrat, the former CEO of private French trading group Louis Dreyfus who used to run its Neuf Cegetel telecoms unit.<br><br>Veyrat left Louis Dreyfus in 2011 with a golden parachute of 270 million euros, according to the French press. He has since set up the Impala group, which invests in companies in distress.<br>Veyrat, Swire, Lion Capital and Change Capital declined to comment, as did Lancel and Richemont.<br>People close to the talks say the bidding process for Lancel, which had already been going on for months, could last several more weeks.<br><br>Lancel is run part-time by Fabrizio Cardinali, CEO of Dunhill, another Richemont brand.<br>Lancel has hired a new designer, Nicole Stulman, who was previously at Reed Krakoff, Hermes (HRMS.PA) and Celine and does not have a head of merchandising to work with since that person has left for Dunhill, sources close to the sale process said.<br><br>Other key people at the company are either on sick leave or have not been replaced, the sources said.<br>Lancel's difficulties come as the luxury sector as a whole remains resilient despite a [http://Www.Alexa.com/search?q=slowdown&r=topsites_index&p=bigtop slowdown] in China, continuing to grow, although at a slower pace than in previous years.<br>PRIVATE EQUITY<br>The relationship between private equity and fashion brands can be difficult because the typical three- to five-year investment horizon may be too short to turn a label around.<br><br>Private equity deals are usually financed by debt, which puts pressure on the fashion brand when it needs to invest in marketing and new shops.<br>Lanvin, acquired by Taiwanese media magnate Shaw-Lan Wang  [http://www.pcs-systems.co.uk/Images/celinebag.aspx http://www.pcs-systems.co.uk/Images/celinebag.aspx] from L'Oreal in 2001, took more than seven years to become profitable. TPG struggled for nine years to restructure the leather goods brand Bally before selling it in 2008.<br><br>There have been few successful revamps of struggling brands that are still going concerns. Carven, Balenciaga and Lanvin lay dormant for decades before they were acquired, allowing their new owners to make a fresh start.<br>Lancel was founded by accessories designer Ang�le Lancel in 1876, remaining in the hands of her [http://www.Wikipedia.org/wiki/descendants descendants] until it was acquired in the late 1970s by the Zorbibe brothers, who with then chief executive Sidney Toledano, now Dior CEO, launched the hit bucket-shaped Elsa bag and made Lancel a profitable business.<br><br><br>Industry executives say Lancel was making margins higher than Louis Vuitton - today's market leader - when Richemont bought it in 1997.<br>"All my girlfriends in the 1990s dreamt of having a Lancel bag," said Serge Carreira, who lectures on luxury at the Institut d'Etudes Politiques in Paris, known as "Sciences Po".<br><br>Lancel had not expanded internationally or creatively as its rivals did, he said.<br>Lancel makes more than 80 percent of its sales in France and in the year to end June, it had an operating loss of 10 million euros on revenues of 135 million euros, sources close to the matter said.<br>Richemont, the world's second biggest luxury group, does not publish separate sales and profit figures for its brands, which include Cartier and Van Cleef & Arpels.<br><br>Longchamp, founded in 1948 and still owned by the founding Cassegrain family, has annual sales of 500 million euros.<br>"ELECTRIC SHOCK"<br>"What Lancel needs in an electric shock in terms of design, marketing, store concept and image," says Boston Consulting Group senior partner Jean-Marc Bellaiche.<br>Analysts say Lancel needs to enter the accessible segment of the luxury market, alongside Coach (COH.N), Michael Kors (KORS.N) and Longchamp with handbags costing 200-800 euros.<br><br>Lancel lost credibility at the high end of the luxury market by offering excessive discounts and putting out staid, old-fashioned designs, such as the Brigitte Bardot bag in 2010 - a 1970s style version of the bucket bag - and the document holder Isabelle Adjani bag in 2008.<br><br>"Lancel's products, while perfectly fine, look a bit dated and are not a must-buy," said Hugh Devlin, a consultant at legal firm Withers LLP, who specializes in luxury and fashion brands.<br><br>"With the right creative team and strategy, that could definitely change but whoever buys it will need to be prepared to take a risk."<br>Lancel clearly thinks it can make it as a luxury brand. A few months ago, it introduced an ostrich leather "L" bag costing 4,500 euros, emulating Gucci (PRTP.PA) and Louis Vuitton's (LVMH.PA) recent efforts to move upmarket.<br><br>Carreira disagrees. "You do not become a luxury brand because you sell a bag for 4,000 euros," he said.<br>To rebuild its name in the crowded accessories market, experts say Lancel should do some ready-to-wear, as Longchamp did, to stimulate traffic in shops and rejuvenate itself.<br>Another potential investor who looked at Lancel said it had suffered from under-investment and excessive management turnover.<br><br>Having had about a dozen chief executives since 1997, the company will now need to be given time by its new owners to implement long-term strategy, industry observers said.<br>(Editing by Giles Elgood)
There are cases in which the alias method is not optimal in rolls of the die. Consider the case where there are two choices with equal probability, and we have a die with 256 sides. The alias method could be performed with one throw of the die. However, the roll of the die could be used to make 8 independent selections between two choices using the binary representation of the numbers from 0 to 255. Another case is when there are a million different choices, but one of the choices has a probability of 99.99%. The alias method would require several rolls of the 256 side die. The table method described by Marsaglia et al. is more efficient.<ref>{{Citation |author1=George Marsaglia |author2=Wai Wan Tsang |author3=Jingbo Wang |title=Fast Generation of Discrete Random Variables |url=http://www.jstatsoft.org/v11/i03 |journal=Journal of Statistical Software |date=2004-07-12 |volume=11 |issue=3 |pages=1–11|accessdate=2012-07-14}}</ref>
 
==Literature==
 
Knuth, Art of Computer Programming, Vol 2: Seminumerical Algorithms: Sect. 3.4.1.
 
==Implementations==
* http://www.keithschwarz.com/darts-dice-coins/ Keith Schwarz: Detailed explanation, numerically stable version of Vose's algorithm, and link to Java implementation
* http://apps.jcns.fz-juelich.de/ransampl Joachim Wuttke: Implementation as a small C library.
 
==References==
{{reflist}}
 
[[Category:Pseudorandom number generators]]
 
 
{{statistics-stub}}
{{comp-sci-stub}}

Revision as of 12:29, 30 January 2014

In computing, the alias method is a family of efficient algorithms for sampling from a discrete probability distribution, due to A. J. Walker.[1] The algorithms typically use O(nlog⁡n) or O(n) preprocessing time, after which random values can be drawn from the distribution in O(1) time.[2]

Internally, the algorithm builds two tables, a probability table and an alias table. To generate a random outcome, a fair die is rolled to determine an index into the probability table. Based on the probability stored at that index, a biased coin is then flipped, and the outcome of the flip is used to determine which result to output.[3]

There are cases in which the alias method is not optimal in rolls of the die. Consider the case where there are two choices with equal probability, and we have a die with 256 sides. The alias method could be performed with one throw of the die. However, the roll of the die could be used to make 8 independent selections between two choices using the binary representation of the numbers from 0 to 255. Another case is when there are a million different choices, but one of the choices has a probability of 99.99%. The alias method would require several rolls of the 256 side die. The table method described by Marsaglia et al. is more efficient.[4]

Literature

Knuth, Art of Computer Programming, Vol 2: Seminumerical Algorithms: Sect. 3.4.1.

Implementations

References

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  1. ↑ A. J. Walker, Electronics Letters 10, 127 (1974); ACM TOMS 3, 253 (1977)
  2. ↑ Vose, Michael. A Linear Algorithm For Generating Random Numbers with a Given Distribution
  3. ↑ Darts, Dice, and Coins: Sampling from a Discrete Distribution. KeithSchwarz.com. Retrieved on 2011-12-27.
  4. ↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

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