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Journal of Statistical Science and Application 2 (2014) 37-46 The Beta Power Exponential Distribution Kazeem A. Adepoju, Chukwu, A.U Department of Statistics, University of Ibadan, Nigeria Min Wang Michigan Technology University, USA A new three-parameter beta power distribution is introduced and studied. We derive formal expressions for its moments, generating function and Cumulative density function. The maximum likelihood estimation of the model parameters was also conducted. In the end, the superiority of the new distribution over the exponentiated exponential was made by means of data set. Key words: Exponential distribution, Beta power exponential, exponentiated exponential, maximum likelihood Introduction In recent time probability distributions play a significant role in modeling naturally occurring phenomena. By this, different kinds of distribution functions have been propounded and defined extensively in the statistical literature in modeling many real life phenomena. Various distributions emerge from the need to capture some naturally occurring events. For instance, Pareto distribution has been justified in modeling the size of companies, family income size, and population size among others. Poisson distribution can be used to measure the occurrence of rare events; Weibull and gamma have been identified as good distributions in modeling the amount of rainfall in African among other functions. Probability distributions revealed lately involve compounded beta family of distribution which include beta-normal Eugene (2002); beta-Gumbel [Nadarajah and Kotz (2004)], beta-Weibull [Famoye (2005)], beta-exponential [Nadarajah and Kotz (2006)]; beta- Rayleigh [Akinsete and Lowe (2008)]; beta-Laplace [Kozubowski and Nadarajah (2008)]; beta-Pareto [Akinsete (2008)]; Kumaraswamy Pareto [Marcelo Bourguignon, etal (2012)], beta Nakagami [Shittu and Adepoju(2013)] among others. The New Distribution A random variable X is distributed as the Beta power exponential distribution if it satisfies the probability density function given as follows; () ( ) ( ) ( ) 1 1 1 1 , + + = b x a x b a x f λ λ β λ (1) This can be showed to be a proper density function as below Corresponding author: Kazeem A. Adepoju, Department of Statistics, University of Ibadan, Nigeria, E-mail: [email protected]. Chukwu, A.U, Department of Statistics, University of Ibadan, Nigeria, E-mail: [email protected]. Min Wang, Michigan Technology University, USA, E-mail: [email protected]. DAVID PUBLISHING D

Contentsretailers.kalmbach.com/sitefiles/catalogsamples/62922spread.pdf · Re-create the look of jewelry worn by Russian tsarinas Marquise de lis ... Use a button as a cabochon, and

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Page 1: Contentsretailers.kalmbach.com/sitefiles/catalogsamples/62922spread.pdf · Re-create the look of jewelry worn by Russian tsarinas Marquise de lis ... Use a button as a cabochon, and

Contents

Introduction..................................................... 8

Tools.&.Materials............................................. 9

Basics..............................................................12

Stitching......................................................... 20Dimensional diamonds ............................................................. 22Stitch diamond shapes into a peyote pattern to create a textured cuff

Wave ring .................................................................................. 24Put beading leftovers to use in these delightful rings

River of light ............................................................................. 26Link crystal stones to make a bracelet that flows gracefully around your wrist

Wildflower vine ......................................................................... 29Create a bell-shaped wildflower using sculptural peyote

Royal jewels ............................................................................. 34Re-create the look of jewelry worn by Russian tsarinas

Marquise de lis ......................................................................... 38So simply sophisticated, you’ll want to make one in every color

Pools of light ............................................................................. 42Dive in! Make a splash with sparkling rivoli ponds surrounded by droplets of beaded fringe

Peyote paradise ....................................................................... 46Flat, circular, and increasing peyote stitch create a flourish of beadwork

Zigzag bangle ........................................................................... 51Turn a craft-store find into a beaded bangle

Scalloped lace .......................................................................... 54Modify right-angle weave so that it curves gracefully

Heavy metal .............................................................................. 56Create substantial links with metal seed beads, then connect them with jump rings

Broad band ............................................................................... 58Communicate your style loud and clear with metallic seed beads and crystals

Victorian sparkle ....................................................................... 61Surround a large crystal stone with layers of seed beads, bicones, and briolettes

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Diagonal view ........................................................................... 64Offset four-bead clusters to shift the color pattern

Cabled bracelet ........................................................................ 66Adapt herringbone stitch with a classic fiber technique for an undulating bracelet

Link to creativity ....................................................................... 68Clever links connect your favorite colors

Dragon alert! ............................................................................. 70Two dragon heads meet nose to nose in a fanciful choker

What’s the buzz? ...................................................................... 74Work St. Petersburg chain forward and backward for a zigzag effect that can be playful or sophisticated

Regal reiteration ....................................................................... 78Make this stately collar of fanning pearl dangles, and you’ll soon know St. Petersburg chain inside and out

Web of silver ............................................................................. 82Metallic seed beads enhance silver focal beads and findings

Golden formula ......................................................................... 84Tubular netting surrounds a strand of oversized beads in this bodacious bangle

Creative networking ................................................................. 88Embellish a flexible base of netting with gemstones nestled in an abundance of seed bead loops

Through & through .................................................................... 91Layers of interlocked scallops create a beautiful collar

Row by row .............................................................................. 94Combine stringing with an easy weaving technique for stunning results

Fascinating fasteners ............................................................... 96Make otherwise inconspicuous buttons the focus of your design

Treasure box ............................................................................. 98Weave together a bounty of crystals

Blooming beaded beads ........................................................ 100Stitch a handful of crystals into gorgeous beaded beads

Lunar illusion .......................................................................... 102Create a constellation of crystals around a solar system of cabochons

Vintage blooms ....................................................................... 106Imitate the look of Miriam Haskell jewelry with bead-embroidered lace

Button fan ............................................................................... 110Use a button as a cabochon, and stitch bead embroidery to mimic the fan-shaped designs on its surface

Fleur de Paris ......................................................................... 115Fashion a feminine flower with a little French flair

Bold buttons ........................................................................... 118Beaded buttons make perfect mini canvases for experimenting with color, design, and texture

Triple time ............................................................................... 120Create three identical beaded-ring components to make a necklace that combines stitching with a bit of wirework

Plaited spiral ........................................................................... 123A double-spiral rope gives a graduated necklace the look of intertwined strands

Hexagonal pillow earrings ...................................................... 126Dangle traditional Chinese pillows from a pair of handmade earring findings

Ice blossoms .......................................................................... 129Adorn yourself with this feminine necklace

Barred bracelet ....................................................................... 132Vertical embellishments are easy to achieve when you combine bead stringing and stitching techniques

Flowering fringe ...................................................................... 134String a full but delicate garland for your wrist

Piecework ............................................................................... 136Curvaceous components create a geometric cuff

Eye of the twister .................................................................... 139The rivoli in the center of an embellished peyote bezel serves double duty as a clasp and focal point

Hibiscus twist ......................................................................... 142Interchangeable flower pendants give you plenty of options

Harmonious array ................................................................... 146Spirals, links, and loops unite for an elegant showpiece necklace

Pearl orbit ............................................................................... 150Combine tubular peyote stitch and tubular herringbone for an opulent wrist adornment

Royal ring ............................................................................... 154Give a round crystal stone the royal treatment

Red herring flower .................................................................. 157Button up a cute little necklace

Byzantine translation .............................................................. 162Stitch a beaded version of Byzantine chain mail

Fanciful romance .................................................................... 166Turn up the heat with fire-polished beads, and fan the flames of fantasy

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Time for teapots ..................................................................... 169Set a miniature beaded teapot on a shelf or wear it as a pendant

Catch a star ............................................................................ 174Rounds of netting capture sparkling crystals and create versatile components

Hojas inspiration ..................................................................... 178Repeat a stylized leaf motif to make a pretty pendant

Wirework...................................................... 180Raining petals ......................................................................... 182Beaded dangles evoke petals gently dropping from a blossoming tree

Dangle delight ........................................................................ 184Crystals and freshwater pearls form sparkling spikes around semiprecious briolettes

Modest exhibition ................................................................... 186Use a minimalist approach to feature a brilliant gem in a graceful wire setting

Queen’s ring ........................................................................... 188Seed beads and crystals add a hint of color to a ring of coiled wire

Lovely lines ............................................................................. 190Give your lobes some love with these stylish adornments

Get in the groove .................................................................... 192Wire welcomes beads with an open embrace

Chained melody ..................................................................... 194Create harmonious balance with linked loops and assorted chain

Sew wired ............................................................................... 197Use twisted wire to sew five antique shell buttons into a necklace

Flight of the butterfly .............................................................. 200Combine gemstones, pearls, and several types of wire for a pendant as eye-catching as its inspiration

Rosy posy pendant ................................................................ 204Use a round loom to bring a wire flower into bloom

Bloomin’ flower ring ............................................................... 208Decorate your digits with layers of colorful beads

Grand Victoria Christmas trees .............................................. 211Warm up with a pair of holiday earrings that hearkens back to the good ol’ days

Copper cascade ..................................................................... 212Interlocking wire-wrapped components and accent beads flow into each other like a stepped waterfall

Perfect pairing ........................................................................ 215Full Persian chain mail sections frame lampworked focal beads

Color division .......................................................................... 217Make the move from flat to tubular chain mail with one additional step

Crystal constellations ............................................................. 220Join jump rings for a galaxy formed by your imagination

Dotty dangles ......................................................................... 222Petite buttons dance on easy layered earrings

Other.Techniques........................................ 224Let’s twist again ...................................................................... 226Use basic crochet techniques to make a casual necklace

Winter medley ........................................................................ 228Embellish a crocheted rope with several fringe techniques

Balancing act .......................................................................... 232Clean lines showcase intricate art-glass beads

Beaded purse revival .............................................................. 235Learn the bead knitting technique of plaited knitting

Knots of fun ............................................................................ 240Try your hand at five different Chinese-style knots

Simple exchange .................................................................... 243Discover how easy it is to make an eight-strand braid of beads

Loops & lace ........................................................................... 246Learn traditional tatting for a sparkling necklace that brings together the best of fiber and beads

Frost relief ............................................................................... 249Acid-etch a glass bead to create a luminous glow

Contributors................................................. 252

Index............................................................. 255

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b

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Peyote stitch

PEYOTE STITCH

Riveroflight

Link crystal stones to make a bracelet that flows gracefully around your wrist

designed by Karen Joelson

stepbystep

[1] On1yd.(.9m)ofthread,pickup24110cylinderbeads,andtiethemintoaringwithasquareknot(Basics,p.12),leavinga6-in.(15cm)tail.Sewthroughthefirstfewbeads,andpulltheknotintothebeadwork.[2] Workingintubularpeyotestitch(Basics),workoneroundusingonecylinderperstitch,andstepupthroughthefirstcylinderinthenewround(figure 1, a–b).[3] Workoneroundusingone150seedbeadperstitch(b–c).Workwithfirmtensionsotheedgeofthebeadworkbeginstopullin(photo a).Workoneroundusingone150Charlotteperstitch(c–d).Snugupthebeadworksoitiscup-shaped(photo b).[4] Sewthroughthebeadworktoexitacylinderontheoppositeedge.Placeacrystalstoneintothebeadwork,thenrepeatstep3toenclosethestone.

[5] Sewthroughthebeadworktoexitacylinderinthemiddleroundofcylinders.Pickupacylinder,andsewthroughthenextcylinderintheround(photo c).Usingonecylinderperstitch,workaroundofpeyote,sewingthroughthecylindersinthemiddleround(photo d).Stepupthroughthefirstcylinderaddedinthenewround.[6] Workoneroundusingtwo150seedbeadsperstitch(figure 2, a–b),workoneroundusingonecylinderperstitch(b–c),andthenworkaroundusingone2.5mmmetalbeadperstitch(c–d).[7] Lookatthebacksurfaceofthebezel.Everyothercolumnofbeadshasastackofthreecylinders.Sewthroughthebeadworktoexitthemiddlecylinderinastack(photo e).[8] Pickupa150seedbead,andsewthroughthecylinderandthe150again(photo f).Workinginladderstitch(Basics),workfivemorestitchestomakealadderthatissix150seedbeadslong.Zigzagbackthroughthe

a b c

Crystalstonessetinbeadedbezelsmakeaglamorousstatement,butifyouwantatailoredlookratherthanalotofcrystalfringe,trythisbracelet.Therepeatingcircularthemethatisechoedinthemetallinkscreatesacalmingeffect.

d e f

fIgurE 1

fIgurE 2

EDITOR’s nOTE:It may seem unlikely, but square stones work fine in this project. Just be sure to use the ones with rounded corners instead of sharp corners.

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knot

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Right-angle w

eave

55

FIGURE 3

ModIFIEd RIGht-AnGlE WEAvE

ScallopedlaceModify right-angle weave so that

it curves gracefully

designed by Donna Pagano Denny

stepbystep

[1] On3yd.(2.7m)ofFireline,pickuparepeatingpatternofa150seedbeadandacolorA4mmbiconecrystalfourtimes,leavinga6-in.(15cm)tail.Tiethebeadsintoaringwithasurgeon’sknot(Basics,p.12).Sewthroughthefirst150again(figure 1).[2] Tocreateapicot,pickupthree150s,sewthroughthe150yourthreadisexiting(figure 2, a–b),andcontinuethroughthenext4mmand150(b–c).[3] Repeatstep2threetimes,andsewthroughthefirsttwo150saddedinstep2(c–d).

[4] Pickupa4mmanda150threetimes,thenpickupanother4mm.Sewthroughthe150yourthreadisexitingandthenext4mmand150again(d–e).[5] Repeatstep2threetimes(e–f),andsewthroughthebeadworktoexitthepicotoppositethepreviousunit(f–g).[6] Repeatsteps4and5threetimes,butafterthethirdrepeat,exitthethree150sadjacenttothe150sjoiningthepreviousunit(figure 3, a–b).[7] Repeatsteps4and5,butinstep5,exitthethree150sadjacenttothe150sjoiningthepreviousunit(b–c).

[8] Repeatsteps4and5tocompletefourmoreunits,butinthelastrepeat,exitthethree150sadjacenttothe150sjoiningthepreviousunit(c–d).[9] Repeatsteps7and8seventimes,endingandaddingthread(Basics)asneeded.Ifyourworkingthreadislessthan24in.(61cm)long,endthethreadsonbothendsofthenecklace,andadd24in.(61cm)ofthreadononeend.[10] Sewthroughthebeadworktoexitthecenter150ontheedgepicotinthefirstunit(figure 4, point a).[11] PickupacolorB4mmbiconecrystal,andsewthroughthetop150inthenextunit(a–b).Repeatthreetimes(b–c),andsewthroughthebeadsinthenextunittoexitthecenter150adjacenttopointc(c–d).[12] PickupanA,andsewthroughthecenter150inthenextedgepicotadjacenttothe150sthatjoinedthepreviousunit(d–e).Sewthroughthebeadworkasshown(e–f).

[13] Repeatsteps11and12eighttimes.Endthethread.[14] Openajumpring(Basics),andattachoneofthepicotsattheendofthenecklacetooneoftheloopsofatwo-to-onefinding.Repeatwithasecondjumpringandthesecondloopofthesametwo-to-onefinding(figure 5).Repeatontheotherendofthenecklace.Attachasplitringtotheremainingloopofeachtwo-to-onefinding.Attachthelobsterclawclasptooneofthesplitrings.w

FIGURE 1 FIGURE 2

FIGURE 4

FIGURE 5

Createaglamorousnecklacethatfallsinscallopsofsparklingcrystals.Thiscollarisperfecttoaccentuateelegantattire.

Designer’s note: For a more casual style, try 3 mm or 4 mm crystal pearls in place of the 4 mm crystals.

materialsnecklace 14 in. (36 cm)• 4mmbiconecrystals 188colorA 36colorB• 5g150Japaneseseed beads• lobsterclawclasp• 2 two-to-onefindings• 43mminside-diameter 20-gaugejumprings• 23–4mmsplitrings• Fireline6lb.test• beadingneedles,#12• 2pairsofpliers

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186 187

Wirew

ork

Let the brilliance of a gemstone shine when you capture it in a wire setting that leaves all its facets exposed.

stepbystep

Pendant bezel and bail[1] Cut a 7-in. (18 cm) piece of 22-gauge square wire, and use roundnose pliers to make a small hook at one end. Use your fingers and chainnose pliers to form a small spiral around the hook (photo a). This spiral will sit against the front of the gemstone.

[2] Position the spiral as you would like it placed against the stone. Without bending the wire, rock the wire back so it is flat against the back of the stone and the spiral is pointing up. Hold the wire tight against the back of the stone, and bend the wire up and around the bottom edge of the stone so that you cross the corner opposite the starting spiral (photo b).

designed by Lilian Chen

Use a minimalist approach to feature a brilliant gem in a graceful wire setting

[5] To make a bail, cut a 2-in. (5 cm) piece of 22-gauge square wire, and make a four-wrap coil at the end using roundnose pliers. Because the pliers are tapered, you’ll need to adjust the position of the wire with each turn so the coils are consistent in size (photo e).[6] Bend the wire down from the coil, and begin curving the wire back up. Attach the pendant to the hook (photo f), and finish with a decorative spiral.[7] On a head pin, string a 10 mm pearl, and make the first half of a wrapped loop (Basics, p. 12). Attach the dangle to the bottom of the pendant, and complete the wraps (photo g).

Leaf connector[1] Cut a 10-in. (25 cm) piece of 22-gauge square wire, and make a four-wrap coil at one end, as in step 5 of “Pendant bezel and bail.”[2] Holding the coil with the long tail on the left, bring the wire down under the coil to the right. Shape the wire into a curve with your fingers, and make an upward bend about 1 in. (2.5 cm) from the coil,

Modestexhibition

materialsnecklace 16 in. (41 cm)• 12x15mmgemstone orcubiczirconia,undrilled• 10mmpearl• 23mmaccentbeads• clasp• 19in.(48cm)22-gauge squarewire,half-hard• 4in.(10cm)24-gauge wire,half-hard• 11⁄2yd.(1.4m)cable chain,2–3mmlinks• 11⁄2-in.(3.8cm)headpin• chainnosepliers• roundnosepliers• wirecutters

cba

fe

d

i

hg

using your pliers as needed. Slide the bail onto the wire, so the front of the pendant is facing you, and feed the end of the wire through the coil made in step 1. Gently pull the wire through the coil, shaping the loop into a leaf shape (photo h). Keep in mind that this segment will hold both the pendant and part of the necklace chain.[3] To make the second leaf segment, curve the wire exiting the coil downward, and make a U-shaped bend about ¾ in. (1.9 cm) from the coil. Feed the wire through the coil, shaping the segment into a leaf as you pull (photo i).[4] Bend the wire up, away from the coil. Make a U-shaped bend about 1 in. (2.5 cm) from the coil, and feed the wire through the coil, creating the third leaf

shape (photo j). Keep in mind that this leaf will hold part of the necklace chain.[5] Bend the wire up, under the third leaf, and curve the end into a spiral (photo k). Use your fingers to gently shape the connector as desired.

Assembly[1] Determine the finished length of your necklace, subtract 1 in. (2.5 cm), and cut two pieces of chain to this length. These pieces will form the long side of the necklace.[2] Measure the length of your leaf connector, and multiply this length by two. Subtract this length from the chain length determined in step 1, and cut two pieces of chain to the new length for the short side of the necklace. (In this

necklace, the long chains were 15 in./38 cm and the leaf connector was 11⁄2 in./3.8 cm, so the short chains were 12 in./30 cm each.)[3] Cut a 2-in. (5 cm) piece of 24-gauge wire, and make the first half of a wrapped loop. Attach an end link of each long chain, and pass the chains through the first leaf of the connector. Be careful not to go through the pendant bail or twist the chains. Attach the remaining end links to the loop, and complete the wraps. [4] String a 3 mm accent bead, and make the first half of a wrapped loop. Attach half of the clasp, and complete the wraps.[5] Repeat steps 3 and 4 with the short chains, passing through the third leaf of the connector instead of the first. w

j k

[3] Pull the wire around the back of the stone to the starting point, and cross the wire in front of the spiral end, just behind the top edge of the stone. Fold the spiral down over the wire and the top edge of the stone, so it sits securely on the front (photo c).[4] Bend the wire back over the spiral and the top of the stone. Use roundnose pliers and your fingers to coil and curve the wire over the top of the stone. Trim the wire as needed, and use roundnose pliers to make a small hook at the end. Secure the hook to the wire along the edge of the stone (photo d).

wirework